On the Fragility of Third-party Punishment: The Context Effect of a Dominated Risky Investment Option
11 ON THE FRAGILITY OF THIRD-PARTY PUNISHMENT: THE CONTEXT EFFECT OF A DOMINATED RISKY INVESTMENT OPTION a Changkuk Im b and Jinkwon Lee c This version: February 8, 2021
Abstract
Some studies have shown that third-party punishment (TPP) substantially exists in a controlled laboratory setting. However, only a few studies investigate the robustness of TPP. This study experimentally investigates to what extent TPP can be robust by offering an additional but unattractive risky investment option to a third party. We find that when both the punishment and investment options are available, the demand for punishment decreases whereas the demand for investment increases. These findings support our hypothesis that the seemingly unrelated and dominated investment option may work as a compromise and suggest the fragility of TPP.
JEL Classification : C72, C92, D87, D91
Keywords : third-party punishment, dominated risky investment, context effect, compromise effect, neuroeconomics a This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors obtained IRB approval from Sogang University (SGUIRB-A-1710-34). b Changkuk Im. Department of Economics, The Ohio State University, Columbus, 43210, U.S.A. Email: [email protected]. c Corresponding author, Jinkwon Lee. School of Economics, Sogang University, Seoul, 04107, South Korea. Tel. +82-2-705-8511. Email: [email protected]. ORCID: 0000-0002-5695-1556
1. INTRODUCTION
Third-party punishment (TPP) is known to be an important way of enforcing people to abide by social norms and achieving social stability (Gintis et al. 2003; Fehr and Fischbacher 2003, 2004a). Indeed, a few experimental studies found the substantial existence of TPP in a controlled laboratory setting (Fehr and Fischbacher, 2004b; Bernhard et al., 2006; Henrich et al., 2006; Marlowe et al., 2008; Ottone et al., 2015). Moreover, it has been known that the main driver of TPP is the third party’s anger triggered by witnessing a violation of social norms such as unfair dictator allocations in a dictator game (Fehr and Fischbacher, 2004b; Nelissen and Zeelenberg, 2009; Jordan et al., 2016). However, several experimental studies have suggested that the existence of TPP is not robust (Balafoutas et al., 2014; Lewisch et al., 2011; Nikiforakis and Mitchell 2014; Carpenter and Matthews, 2012). Thus, to what extent TPP can be robust in a laboratory setting is worthy to be examined. In this paper, we experimentally test the robustness of TPP by offering a seemingly unrelated and unattractive alternative in addition to a punishment option to a third party. If this unfavorable option even deters the demand for TPP, then we can say that the motivation of TPP is fundamentally fragile. In our three-player dictator game, similar to the experimental design of Fehr and Fischbacher (2004b), we offer a third party an opportunity to punish a dictator with a material cost after observing the dictator’s allocation. In addition to the punishment option, we provide a third party a simple risky investment option that its expected net return is equal to or less than zero. Note that from the perspective of material payoffs, risk-averse third parties should not invest in this Third-party punishment (TPP) refers to an individual’s behavior when one is willing to impose costly punishment to a norm violator even if ones’ payoff is not affected by the violator. lottery. From the perspective of psychological payoffs, the investment option, compared with the punishment option, is not the best instrument for venting negative emotions such as anger. Hence, at first glance, the investment option that we additionally offer seems unlikely to affect risk-averse and risk-neutral third parties’ behavior because it is a dominated option in terms of both material and psychological payoffs. However, combining neuroeconomic studies on the risky decision-making, punitive behaviors, and compromise effect opens a possibility of the dominated investment option to work as a compromise and affect a third party’s punishment decision. According to those studies, the parts of the brain such as the prefrontal cortex and the anterior insula are commonly activated for risky, punishment, and context-dependent choices, including compromise choices. Although conjecturing a cognitive functioning simply through the activated area of the brain is difficult (Poldrack 2006, 2010), the co-incidental activations in similar areas by different environmental stimuli can still be interacted and confound the role of the brain (Singer et al. 2009; Genon et al. 2018). This possibility suggests that a context effect can play a crucial role when both punishment and investment alternatives are available. In particular, assuming that material and psychological payoffs are two distinguished attributes involved in a third party’s decision-making process, the dominated investment option could be perceived as an intermediate choice in both attributes and hence become more attractive. Thus, by this compromise effect, the A compromise effect refers to the phenomenon of the people’s tendency to choose an intermediate option in all attributes rather than the extreme options in a given choice set (Simonson 1989). It has been widely examined in marketing, psychological, and economic studies (Dhar and Simonson 2003; Lichters et al. 2016; Pinger et al. 2016; Trueblood et al., 2013). These studies include Shiv et al. (2005), Hu and Yu (2014), Hedgcock and Rao (2009), Shafir et al. (2002), Mohr et al. (2017), Kuhnen and Knutson (2005), Paulus et al. (2003), Bechara et al. (2005), Preuschoff et al. (2008), Krueger and Hoffman (2016), Sanfey et al. (2003), de Quervain et al. (2004), and Ginther et al. (2016). The detailed discussions are presented in Section 4. demand of TPP would be smaller when both the punishment and the investment options are available relative to the demand of TPP when the investment option is not allowed. In our experiment, we find that both the choice frequency and the expenditure of punishment significantly decrease when a third party is allowed to choose the dominated investment option as well. Additionally, when all options are available, we find that the choice frequency and the expenditure of investment tend to increase. The increased demand for investment supports that the reduced demand for TPP is not an experimenter demand effect caused by the difference in the number of available alternatives. Instead, our main findings weakly support the hypothesis that the investment option works as a compromise and confirm that TPP is indeed susceptible to such a context effect. Our finding of the fragility of TPP contributes to the existing literature in several aspects. First, although TPP clearly exists in an experimental setting, our results imply its sensitivity to the design of an experiment. This finding would help a researcher design a decent experiment and analyze the data properly when exploring TPP. Second, in terms of external validity, our results suggest another fundamental reason why TPP is rare in the real world (Guala, 2012; Balafoutas and Nikiforakis, 2012). Specifically, given that multiple types of alternatives exist in the real world, the context effects are likely to be associated with a third party’s decision and eventually deters the motivation of TPP. Lastly, consistent with the recent findings from neuroeconomics, our results provide additional evidence that both material and psychological payoffs matter in a decision context where both punishment and risk attitudes are involved. This further suggests that context effects usually studied in the areas of marketing and consumer decisions can be well applied to the field of prosocial behavior. The remainder of this paper is organized as follows. Section 2 reviews related literature on
TPP. Section 3 describes our experimental design. Section 4 presents hypotheses based on a contextual model. Section 5 analyzes the experimental results. Section 6 concludes the paper.
2. RELATED LITERATURE
Fehr and Fischbacher (2004b) conducted the first experiment investigating the existence of TPP. They modified a dictator game and a prisoner’s dilemma game by adding a third party and found that about 60% of third parties punish subjects who allocate an unequal amount of endowment in the dictator game or choose not to cooperate in the prisoner’s dilemma game. After this seminal study, several experimental studies have replicated this finding (Bernhard et al., 2006; Henrich et al., 2006; Marlowe et al., 2008; Ottone et al., 2015). However, a few studies raised a question about the robustness of the existence of TPP. For instance, Balafoutas et al. (2014) showed a significant decrease in the demand for TPP when a third party has a risk of being counter-punished by a norm-violator. Moreover, Lewisch et al. (2011) showed a decrease in third party’s willingness to punish if a group has an additional potential punisher. Some studies have found that the demand for punishment decreases when alternative options such as rewarding a norm abider or second-party punishment (SPP) in addition to a punishment opportunity are given to a third party (Nikiforakis and Mitchell, 2014; Carpenter and Matthews, 2012). Although we also offer an alternative to a third party, the novelty of our experiment is that the additional option we provide is seemingly unrelated to prosocial behavior and unattractive to most third parties in terms of both material and psychological payoffs. Hence, if the demand for TPP significantly decreases in our experiment, Second-party punishment (SPP) refers to an individual’s punitive behavior toward a violator or a deviator who affects the punisher’s payoff (Fehr and Gächter, 2000). we can say that TPP is fragile and sensitive to a given decision context. Answering the question of whether TPP is robust under diverse circumstances is important to improve our understanding of human prosocial behavior. For instance, findings that dictator allocations are sensitive to experimental designs in dictator games suggest that rules of fair allocation in the game differ by context, are not broadly shared across individuals, and are often in conflict with self-interest. Likewise, the study of robustness test on TPP would contribute to an enhanced understanding of punitive behavior in general. Extending to the real-life implication, Guala (2012) argued that there is scarce evidence that voluntary material punishment, including SPP and TPP, exists in the real world. Similarly, Balafoutas and Nikiforakis (2012) found that less than 5% of people asked a person who deliberately throw out garbage in a subway station to gather the garbage or blamed the transgressor in other ways. One main reason for the low extent of TPP in the field is the presence of a risk to be counter-punished by the violator (Balafoutas et al., 2014, 2016). Our study offers another possible fundamental reason for a low demand for TPP in the real world. That is, the decision-making environment in the field, in which many alternatives exist, opens a wider room wherein a context effect can effectively work. Thus, in the presence of a situation where TPP is required, an alternative choice, which has not been effective, could begin to influence an individual to avoid TPP. In fact, recent studies have found that context effects are substantial in some field decision-making environments (Ashraf et al. 2015; Pinger et al. 2016).
3. EXPERIMENTAL DESIGN AND PROCEDURE In psychological terms, the dictator game having such properties is called “weak situation” (Camerer and Ho, 2015).
The experiment was conducted at SEE Lab (Sogang Experimental Economics Laboratory) at Sogang University, South Korea, using z-Tree program (Fischbacher, 2007). A total of 318 undergraduate and graduate students majoring in various academic fields at the university participated in the experiment. The total number of sessions was 16, and each session consisted of one of five treatments. Each subject participated only in one session.
Each treatment consists of two independent tasks: Task 1 and Task 2. All subjects faced the same Task 1 regardless of treatments. After all the subjects made decisions for Task 1, they faced Task 2. The various treatments in the experiment depended only on Task 2 as explained below. The instructions for Task 2 were displayed after Task 1 was completed, and the contents of the instructions were different depending on treatments and roles in Task 2. The total payoff was accumulated for both tasks. However, the realization of the outcome in Task 1 was conducted after all experiments were completed to mitigate a possible wealth effect. The average duration of each treatment was 40 minutes. The conversion rate was 80 KRW (roughly, 0.08 USD) per token. The show-up fee was 3,000 KRW, and the average earning including the show-up fee was about 12,000 KRW.
In Task 1, we elicited subjects’ risk preference following Holt and Laury (2002). Task 1 consists of individual decision problems of ten paired lottery-choices as presented in Table 1. The payoffs in Lottery L are less variable than the payoffs in Lottery R. Thus, the switching point from Lottery L to R represents the extent of risk-aversion. For instance, for any expected utility framework, switching at Question 5 represents a risk-neutral preference, and a higher switching point represents a higher risk-aversion. [Table 1] At the beginning of Task 2, subjects were randomly assigned to Player A, B, or C, and three distinct types of subjects were randomly matched as a group. Player A (dictator), B (recipient), and C (third party) received endowments of 100, 0, and 50 tokens, respectively. Depending on Player C’s decision problem, we implemented five different treatments denoted as punishment treatment (P treatment), punishment and investment with zero expected net return treatment (P&I0 treatment), investment with zero expected net return treatment (I0 treatment), punishment and investment with negative expected net return treatment (P&Ineg treatment), and investment with negative expected net return treatment (Ineg treatment). P treatment is a generic version of the dictator game with TPP as in Fehr and Fischbacher (2004b). Player A could transfer 0, 10, 20, 30, 40, or 50 tokens to Player B. Then, Player C had an opportunity to impose deduction points on Player A, which is referred to as a “punishment option.” One deduction point costs 1 token and reduces the opponent’s tokens by 3. Thus, if Player C imposes X number of deduction points on Player A, then Player C’s payoff is reduced by X tokens and Player A’s payoff is reduced by 3 times X tokens. Player C’s remaining tokens Technically, switching at Question 5 allows either risk-averse, risk-neutral, or risk-loving preferences. For instance, assuming a utility function 𝑢𝑢 = 𝑤𝑤 ( 𝑟𝑟 ≠ 𝑢𝑢 = ln 𝑤𝑤 ( 𝑟𝑟 = 1), where 𝑤𝑤 is wealth and 𝑟𝑟 is a constant relative risk aversion (CRRA) coefficient, the switching point at Question 5 represents the CRRA coefficient interval ( − . However, since the extent of risk-loving and risk-averse is small, we define an individual who switches at Question 5 as risk-neutral. Moreover, further analysis in Section 5.3 mitigates this issue. All subjects participated in Task 1 regardless of their roles in Task 2. after purchasing deduction points are kept in one’s private account referred to as a “safe option.” Hence, Player C’s decision problem is to allocate the endowment to the punishment option and the safe option. Player C has a distinct choice set for each treatment, whereas Player A’s set of choices is identical across all treatments. In P&I0 treatment, we offered Player C an additional alternative, called an “investment option,” which is similar to Gneezy and Potters (1997). The investment option is a simple lottery that costs one token per point and returns double with half probability or nothing with half probability. Thus, if Player C spends Y tokens on investment points, the payoff is decreased or increased by Y tokens with equal probability. Hence, Player C’s decision problem in this treatment is to allocate the endowment to the punishment option, the investment option, and the safe option. In I0 treatment, we offered only the investment option and the safe option to Player C. Thus, Player C’s decision problem in this treatment is to allocate the endowment to the investment option and the safe option. We additionally implemented P&Ineg and Ineg treatments where a lottery yields a negative expected net return. In particular, the structures of P&Ineg and Ineg treatments are identical to those of P&I0 and I0 treatments, respectively, except for the return rate of the investment option, which is reduced from 2 to 1.5. These two treatments were implemented to check the robustness of the results for the case where a possible indifference between the investment option and the Meanwhile, Player B reported expectations on how many tokens Player A would transfer and how many tokens Player C would use for punishing Player A to an experimenter. Obviously, these guesses did not affect anyone’s material payoffs at all. Player B reported expectations as in P treatment but included additional guessing on how many tokens Player C would purchase for investment points. Clearly, the expectations had no effect on any subject’s material payoffs. Player B, likewise, reported expectations about Player A’s transfer and Player C’s investment decisions. The guesses had no effect on any subjects’ material payoff. safe option is excluded. Further, the supplementary treatments can remove the possibility of safe option’s non-dominance over investment option in terms of material payoffs. This possibility can occur because of either the risk elicitation method that we used in Task 1 or the discrepancy of risk attitudes from different risky tasks used in Tasks 1 and 2. Details are explained in Section 4. Table 2 summarizes available alternatives in each treatment. [Table 2] In all treatments, we used a strategy method to observe Player C’s choices. This means that Player C had to decide the number of deduction and investment points for all six cases of Player A’s possible transfers, that is, 0, 10, 20, 30, 40, and 50 tokens. To avoid unintended experimenter demand effects, we used neutral words in the instructions. Furthermore, we clarified in the instruction that Player C can spend all, none, or partial amount of the endowment on deduction and/or investment points. We asked control questions to prevent decision-making without fully understanding the experiment; that is, subjects could move on to the actual decision-making screen only if they answered all the questions correctly. Those who wrote wrong answers had to read the instruction again and revise the answer correctly. Instructions and examples of control questions are provided in Appendix A. After Task 2, all the subjects were required to fill out a brief questionnaire, including questions on personality traits and socio-demographic information. After the questionnaire section, they privately received the final payoffs in cash in an enclosed envelope and left the laboratory.
4. CONCEPTUAL FRAMEWORK AND HYPOTHESES For example, we indicated each subject as “Player A,” “Player B,” or “Player C” instead of calling “dictator,” “recipient,” or “third party.” Likewise, we wrote “deduction points” when we explain the role of Player C and never used words such as “punish” or “sanction.” This section discusses the implication of the investment option as a compromise and proposes hypotheses of our experiment based on a contextual model (Kivetz et al., 2004). We assume that an individual has preferences over material and psychological payoffs. Thus, we regard material and psychological payoffs as two distinct attributes. In particular, an individual evaluates an alternative in terms of the material-payoff attribute and the psychological-payoff attribute separately, and then combines them as a whole for the final decision. We assume that an individual’s risk attitude is involved when one evaluates risky alternatives based on the material-payoff attribute. For example, a risk-averse individual ranks the safe alternative higher than the risky alternative in our experiment. Given that TPP is driven by negative emotions such as anger (Fehr and Fischbacher, 2004b; Nelissen and Zeelenberg, 2009; Jordan et al., 2016), we assume that an individual focuses on the emotional venting aspect when one evaluates alternatives based on the psychological-payoff attribute. For example, an individual ranks an alternative higher if it is a good means for expressing one’s emotion. Considering risk-neutral and risk-averse third parties, the investment option is an unattractive choice because it is always dominated by either the punishment option or the safe option in each attribute. Specifically, in terms of the material-payoff attribute, the safe option is the best, the investment option is the second-best, and the costly punishment option is the worst. From the perspective of the psychological-payoff attribute, the punishment option is the best because it is a good instrument to directly express one’s negative emotions and oppositions after observing a dictator’s unfair allocation (Fehr and Fischbacher, 2004b; Nikiforakis and Mitchell, 2014; Dickinson and Masclet, 2015). By contrast, the safe option would be the worst because keeping In Appendix B, we use a normalized contextual concavity model studied by Kivetz et al. (2004) to formally demonstrate how the compromise effect can work in our experiment. Relevant propositions and proofs are also presented in Appendix B. one’s endowment in the private account means literally doing nothing. Given that a risky alternative could indirectly improve the emotional state with an impulsive risk-taking behavior (Tice et al., 2001), we argue that the investment option is the second-best choice in terms of the psychological-payoff attribute. Note that although the investment option is always dominated by another alternative in each attribute, it is also an intermediate choice under all attributes. Therefore, if a compromise effect works, then third parties want to invest in the lottery rather than to punish a norm violator when all the three alternatives are available. One may reasonably argue that, for some risk-neutral and risk-averse individuals, the investment option with zero expected net return is not dominated by the safe option in terms of the material-payoff attribute. One reason is from the risk elicitation method in Task 1. The way we define “risk-neutral” in Task 1 allows some extent of “risk-loving” attitudes. Thus, some “risk-loving” third parties, yet defined as “risk-neutral” in Task 1, would evaluate the investment option better than the safe option in terms of the material-payoff attribute in Task 2. Another reason is from the distinct risk elicitation methods in Tasks 1 and 2. Crosetto and Filippin (2016) found that the degree of risk aversion elicited by Holt and Laury (2002) tends to be higher than that by Gneezy and Potters (1997). We follow the design of Holt and Laury (2002) in Task 1 and provide a lottery that is similar to Gneezy and Potters (1997) in Task 2; thus, an individual who is sorted as “risk-neutral” or even “risk-averse” in Task 1 may act like a “risk lover” in Task 2. Hence, those third parties would evaluate the investment option better than the safe option in terms of the material-payoff attribute as well. To deal with this issue, we additionally conduct P&Ineg and Ineg treatments offering a lottery with a negative expected net return for the investment option. Those supplementary treatments allow us to test whether the results from P, P&I0, and I0 treatments are robust or not. Based on the framework discussed in this section, we construct the following hypotheses:
Hypothesis 1.
For the risk-neutral and the risk-averse, the choice frequency and the expenditure of punishment in P&I0 [P&Ineg] treatment are lesser than those in P treatment.
Hypothesis 2.
For the risk-neutral and the risk-averse, the choice frequency and the expenditure of investment in P&I0 [P&Ineg] treatment are greater than those in I0 [Ineg] treatment.
5. RESULTS
In this section, we test our hypotheses using experimental data. Table 3 displays the total number of third parties and their risk attitudes that were elicited in Task 1. Throughout the analysis, we omit observations whose risk preference is inconsistent and focus on risk-neutral and risk-averse Player Cs. [Table 3] Figure 1a reports that, in P treatment, more than 60% (n=23) of risk-neutral and risk-averse Player Cs imposed a positive number of deduction points on Player A who transferred nothing to Player B. This is in accordance with the result of Fehr and Fischbacher (2004b). The percentage is constant until the transfer level of 20 is reached, and it starts to decline so that it approaches zero at the fair allocation. This pattern also appears in P&I0 treatment; that is, roughly 40% We define an individual to have inconsistent risk preferences if he or she makes a switch from Lottery B to A or chooses Lottery A in the last choice problem in Task 1. The results presented in Section 5 are not qualitatively affected even if we consider the entire subjects whose risk preferences are consistent. Analyses for the risk-consistent subjects are summarized in Appendix C.1. In addition, analyses on the transfer behavior of risk-consistent dictators are presented in Appendix D. (n=22) of risk-neutral and risk-averse Player Cs punished Player A at the transfer level of zero, and the percentage approaches zero at the transfer level of 50. Figure 1b reports that, on average, Player C assigned about 15 deduction points in P treatment and 5 deduction points in P&I0 treatment to Player A who transferred nothing. The expenditures monotonically decrease and converge to zero as the transfer level increases in both treatments. [Figure 1] Despite the similar punishing pattern between the two treatments, the percentage points and expenditures considerably differ at unfair transfer levels. Indeed, we find that the percentage of punishers is significantly lower in P&I0 treatment than the percentage in P treatment for each unfair transfer level (all p<0.054 at transfer levels 0–40, chi-square test). The expenditure of deduction points in P&I0 treatment is also significantly smaller than the expenditure in P treatment for each unfair transfer level (all p<0.032 at transfer levels 0–40, two-sided Wilcoxon rank-sum test). Hence, our data show that a third party’s willingness to punish significantly decreases when the dominated investment option is available. [Table 4]
For a thorough examination of the diminished demand for TPP, we also conduct a regression analysis. First, we regress
Punisher on Transfer , Treatment, and other controlling variables using a linear probability model (LPM) and a Probit model. Punisher is defined as 0 if Player C assigned no deduction point and 1 if Player C imposed any positive number of deduction points on Player A.
Transfer contains 0 to 50 with 10 increments.
Treatment is 0 if the treatment is P treatment and 1 if P&I0 treatment. Columns 1 and 2 in Table 4 show that the coefficients of Controlling variables include
Switching point , socio-demographic, and Big Five personality traits.
Switching point is the question number where an individual switch the choice from Lottery L to R in Task 1. Socio-demographic variables include
Gender , Income , and
Economic major . Treatment are negative and significantly different from zero. This implies that the probability of being a punisher is lower in P&I0 treatment than in P treatment. In addition, we define
Punishment as the token amounts Player C spent for imposing deducting points on Player A. Then, we regress
Punishment on Transfer , Treatment, and other controlling variables using ordinary least squares (OLS) model and a Tobit model. Columns 3 and 4 in Table 4 show that the coefficients of
Treatment are negative and significantly different from zero, which implies that the amount of punishment is smaller in P&I0 treatment than in P treatment. [Table 5] Moreover, we examine Player C’s punitive behavior using subjects’ individual-level data. We define a subject’s mean punishment [ mean investment ] as one’s mean expenditure for deduction [investment] points across all transfer levels. Similarly, a subject’s median punishment [ median investment ] is defined as one’s median expenditure for deduction [investment] points across all transfer levels. Analyses on these subject-level data are summarized in Table 5. The averages of mean [median] punishment are 6.88 [7.02] in P treatment and 1.86 [1.36] in P&I0 treatment, and the difference is statistically significant (p=0.012 [p=0.002], two-sided Wilcoxon rank-sum test). Columns 5–8 in Table 4 report the results of OLS and Tobit regressions using the individual-level data. All coefficients of Treatment are negative and significantly different from zero. Thus, results using the individual-level data also support the reduced demand for TPP. As we discuss in Section 4, some risk-neutral Player Cs may not consider the investment option as a compromise because it may not be strictly dominated by the safe option in terms of the material-payoff attribute. Hence, it is worthy to check whether we can observe similar We also include an
Interaction term, which is a product of
Transfer and
Treatment , as an independent variable in the models used in Tables 4 and 6. We find that the
Interaction term does not qualitatively affect the regression results reported in Section 5.1 (See Appendix C.2). punishing behavior by considering the risk-averse only. An analysis reported in Appendix C.3 confirms that the diminished demand for TPP still holds even if we only consider risk-averse third parties. We summarize these findings as follows: Result 1.
Both the frequency of punisher and the expenditure of deduction points decrease when the dominated investment option whose expected net return is zero is available in addition to the punishment option and the safe option. Thus, Hypothesis 1 is supported.
One may argue that an experimenter demand effect of the different number of available alternatives induces the diminished demand for TPP. Specifically, the third party in P&I0 treatment has two available options, namely, the punishment option and the investment option, to avoid doing nothing . Meanwhile, the third party in P treatment has only the punishment option to avoid doing nothing. Then the experimenter demand effect suggests the possibility that the narrower choice set offered in P treatment could induce Player C to spend more tokens for deduction points than in P&I0 [P&Ineg] treatment because one might feel awkward about doing nothing during the experiment. If this is the convincing explanation for Result 1, the investment demand should also be lower in P&I0 [P&Ineg] treatment than in I0 [Ineg] treatment since the choice set in the latter treatment is more restricted. By contrast, Hypothesis 2 predicts that the investment demand should be larger in P&I0 [P&Ineg] treatment than in I0 [Ineg] treatment. The following subsection provides evidence that the investment behavior is indeed consistent with Hypothesis 2, suggesting that the diminished TPP is not an artifact of the experimenter demand effect. Doing nothing here means allocating the entire tokens to the safe option. Figure 1c reports that, for all transfer levels, roughly 60% of risk-neutral and risk-averse Player Cs purchased a positive number of investment points in I0 treatment, whereas almost all Player Cs purchased a positive number of investment points in P&I0 treatment. For each transfer level, the difference in the proportions between the treatments is statistically significant (all p<0.005 at transfer levels 0–50, chi-square test). Figure 1d reports that Player C purchased about 14 investment points, on average, for all transfer levels in I0 treatment. In P&I0 treatment, Player C spent about 22 points, on average, at the transfer level zero and monotonically increased the expenditure as the transfer level rises. For each transfer level, the difference in the expenditures between the treatments is statistically significant (all p<0.041 at transfer levels 0–50, two-sided Wilcoxon rank-sum test). Thus, the data show higher percentage of investors and the expenditure for investment points when the punishment option is also available to Player C than those when only the investment option and the safe option are available. [Table 6] A regression analysis thoroughly confirms the increased demand for investment. We define
Investor as 0 if Player C did not invest in the lottery at all, and 1 if Player C purchased any positive number of investment points.
Investment is defined as the token amount Player C spent for investment points. Independent variables contain
Transfer, Treatment , and other controlling variables. Here,
Treatment is defined as 0 if I0 treatment and 1 if P&I0 treatment. The regression One interesting finding is strictly positive and considerable percentage of investor and investment expenditure in I0 and Ineg treatments. However, recent studies of preferences for randomization (Agranov and Ortoleva, 2017, 2020; Dwenger et al., 2018; Agranov et al., 2020; Feldman and Rehbeck, 2020) can rationalize this investment behavior. For example, if a third party is willing to randomize or mix a safe alternative and a risky alternative, then one would like to allocate some positive token amount to the dominated investment option regardless of one’s risk attitude. Nevertheless, those preferences cannot predict the increased investment demand when the punishment option is available. Hence, our framework in Section 4 is still valid. results of Investor using an LPM and the Probit model are presented in columns 1 and 2 in Table 6. The coefficients of
Treatment are positive and significantly different from zero, which means that the probability of investing in the lottery is higher in P&I0 treatment than in I0 treatment. The regression results of
Investment using OLS and Tobit models are presented in columns 3 and 4 in Table 6. Likewise, the coefficients of
Treatment are positive and significantly different from zero, implying a higher expenditure of investment in P&I0 treatment than in I0 treatment. We also examine Player C’s investment behavior using the individual-level data. According to Table 5, the averages of mean [median] investment are 13.98 [13.63] and 24.05 [24.20] in I0 and P&I0 treatments, respectively, and they are significantly different (p=0.024 [p=0.018], two-sided Wilcoxon rank-sum test). OLS regression results using the individual-level data are presented in columns 5 and 7 in Table 6, and they show that the coefficients of
Treatment are positive but not significantly different from zero. However, if we consider censored data through a Tobit model, then the coefficients are positive and significantly different from zero, as indicated in columns 6 and 8 in Table 6. We further analyze the investment behavior excluding the risk-neutral and considering the risk-averse only. An analysis presented in Appendix C.3 still confirms the increased demand for investment even if we consider risk-averse third parties only. We summarize the findings as follows:
Result 2.
Both the frequency of investors and the expenditure of investment points increase, or at least do not decrease, when all the options are available. Thus, Hypothesis 2 is supported.
Results 1 and 2 clearly show that our findings are not an artifact of the experimenter demand Similar to Section 5.1,
Interaction term does not qualitatively affect the results (See Appendix C.2). effect induced by the different number of alternatives. Instead, a substitution effect seems to exist between punishment and investment, supporting our hypotheses that the investment option works as a compromise. [Table 7] To verify the existence of the substitution effect in more detail, we regress
Investment on Transfer and other controlling variables in P&I0 and I0 treatments, respectively. Given that
Punishment is negatively correlated with
Transfer (Table 4),
Investment and
Transfer in P&I0 treatment would be positively correlated if a substitution effect between punishment and investment exists. This positive correlation between
Investment and
Transfer would disappear in I0 treatment since the punishment option that connects those two variables is not available anymore. Indeed, we find a significantly positive correlation in P&I0 treatment but an insignificant correlation in I0 treatment as presented in columns 1–4 in Table 7. These results support the existence of the substitution effect. Another way to verify the substitution effect is to compare a non-punisher’s investment expenditure in P&I0 treatment with the investment expenditure in I0 treatment. Note that being a non-punisher in P&I0 treatment has two possible reasons. One is that a non-punisher is actually a third party who never chooses to punish in any circumstance. Here, the non-punisher’s decision problem in P&I0 treatment is identical to the decision problem in I0 treatment since the availability of punishment has no impact. The other reason for being a non-punisher is the substitution effect; that is, a third party reduces punishment to allocate more tokens to the investment option when it is available. Consequently, a non-punisher’s investment expenditure would be relatively higher in P&I0 treatment than in I0 treatment if the substitution effect exists; otherwise, the investment expenditures between the treatments would have no difference. Our data show that a non-punisher’s investment expenditure in P&I0 treatment is significantly higher than the expenditure in I0 treatment (all p<0.035 at transfer levels 0–50, two-sided Wilcoxon rank-sum test). We also regress Investment conditional on a non-punisher on
Treatment and other variables. Columns 5 and 6 in Table 7 show that the investment expenditure of a non-punisher is higher in P&I0 treatment than in I0 treatment. Therefore, we have the following result:
Result 3.
A substitution effect exists between the punishment and the investment options, supporting investment option working as a compromise.
As discussed in Section 4, some Player Cs who are sorted as “risk-neutral” or even “risk-averse” in Task 1 might act as if they are “risk lover” in Task 2. Then, the investment option is no longer a compromise to those third parties. To deal with this issue, we conducted supplementary treatments, namely, P&Ineg and Ineg treatments, where the lottery yields a negative expected net return. Note that the investment option offered in these treatments should be dominated by the safe option in terms of the material-payoff attribute even for moderately risk-loving third parties. [Figure 2]
Figures 2a and 2b suggest that risk-neutral and risk-averse Player Cs are less likely to punish Player A in P&Ineg treatment than in P treatment. Indeed, the percentage of punishers is significantly lower in P&Ineg treatment than in P treatment for each unfair transfer level (all p<0.033 at transfer levels 0–40, chi-square test), and the expenditure for deduction points is significantly smaller in P&Ineg treatment than in P treatment for each unfair transfer level (all p<0.038 at transfer levels 0–40, two-sided Wilcoxon rank-sum test). Table 8 presents the averages of punishment using the individual-level data. The averages of mean [median] punishment are 6.88 [7.02] and 1.25 [0.25] in P and P&Ineg treatments, respectively, and the difference is statistically significant (p=0.019 [p=0.003], two-sided Wilcoxon rank-sum test). Related regression results presented in Appendix C.4 indicate the diminished demand for punishment as well. Hence, Result 1 is supported even though the expected net return of the dominated investment option is negative. [Table 8] Figures 2c and 2d suggest that risk-neutral and risk-averse Player Cs are more willing to invest, or at least less likely to reduce investment, in P&Ineg treatment compared with Ineg treatment. The proportion of investors is higher in P&Ineg treatment than in Ineg treatment for each transfer level, and the differences are significant at most transfer levels (all p<0.050 at transfer levels 10, 30, 40, and 50, chi-square test). The expenditure of investment is also higher in P&Ineg treatment than in Ineg treatment for each transfer level, although the difference is significant only at the transfer level of 10 (p=0.029, two-sided Wilcoxon rank-sum test). As shown in Table 8, using the individual-level data, the averages of mean [median] investment are 6.12 [4.86] and 15.08 [15.00] in Ineg and P&Ineg treatments, respectively. Moreover, the difference is marginally insignificant [significant] (p=0.131 [p=0.080], two-sided Wilcoxon rank-sum tests). The related regression results reported in Appendix C.4 support both the increased demand for investment and the existence of a substitution effect between punishment and investment. Therefore, Results 2 and 3 are also weakly supported under the supplementary treatments.
6. CONCLUDING REMARKS
This study experimentally tests whether or not TPP is robust to a context effect, and finds that the availability of the seemingly unrelated and dominated investment option reduces both the choice frequency and the amount of TPP. Moreover, the increased (at least not decreased) demand for investment when both punishment and materially dominated investment options are available in our study indicates a possible substitution effect between the punishment and the investment options. These findings give weak support to the conjecture that the investment option may work as a compromise and confirm the fragility of TPP. An interesting finding in our experiment is that a sizable fraction of risk-neutral and risk-averse third parties choose to invest in a lottery that yields zero or negative expected net return even when the context effect plays no role, that is, when the punishment option is not available. A possible explanation for this behavior is that people may have preferences for randomization (Agranov and Ortoleva, 2017, 2020; Dwenger et al., 2018; Agranov et al., 2020; Feldman and Rehbeck, 2020). For instance, apart from one’s risk attitude, a third party may prefer to mix between the safe option and risky investment option. Then, even risk-averse third parties may allocate some positive token amount to the dominated risky option. The investment behavior in our experiment may be one example why people sometimes choose an unfavorable alternative, and exploring its fundamental motivation would be an interesting further study. Lastly, we address a few more possible future research topics motivated by our findings. We believe that investigating whether TPP is still susceptible to context effects generated by another type of dominated option besides the one used in this study would be interesting. This may strengthen the argument why TPP is difficult to find in the field where multiple types of alternatives exist. Another interesting topic would be to examine whether other prosocial behaviors, such as SPP or rewarding, are robust to context effects. For instance, if rewarding is sensitive to a decision environment as in our study, it could provide a rationale for or against the so-called “Good Samaritan Law,” which enforces bystanders to help an injured person by legally sanctioning an individual who ignores and does not assist the person. REFERENCES
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Choice question Lottery L Lottery R E(L)-E(R) 1 (3,750, 1/10; 3,550, 9/10) (8,000, 1/10; 100, 9/10) 2,680 2 (3,750, 2/10; 3,550, 8/10) (8,000, 2/10; 100, 8/10) 1,910 3 (3,750, 3/10; 3,550, 7/10) (8,000, 3/10; 100, 7/10) 1,140 4 (3,750, 4/10; 3,550, 6/10) (8,000, 4/10; 100, 6/10) 370 5 (3,750, 5/10; 3,550, 5/10) (8,000, 5/10; 100, 5/10) −
400 6 (3,750, 6/10; 3,550, 4/10) (8,000, 6/10; 100, 4/10) − − − − − Table 2. Choice set for each treatment
Available options Treatment Punishment Investment Expected value of investment P Yes No — P&I0 Yes Yes Zero I0 No Yes Zero P&Ineg Yes Yes Negative Ineg No Yes Negative Note: The safe option is always available across all treatments.
Table 3. Sorting third parties based on risk attitudes
Treatment Total P P&I0 I0 P&Ineg Ineg Number of third-parties 27 28 23 13 15 106 Risk attitude: Risk-neutral 7 9 7 3 4 30 Risk-averse 16 13 12 7 7 55 Risk-loving 4 4 3 3 4 18 Risk-inconsistent 0 2 1 0 0 3 Note: Risk attitudes were elicited in Task 1. Table 4. Regression on punishment (with risk-neutral and risk-averse)
Note: The dependent variable in Tobit models is truncated at 0 (left-censored) and 50 (right-censored). Socio-demographic variables include gender, income, and Economics major. In columns 1–4, clustered standard errors at the individual level are in parentheses. In columns 5–8, standard errors are in parentheses. ***, **, and * denote significance at 1%, 5%, and 10% levels, respectively.
Treatment: P, P&I0 Level of data: Transfer level Transfer level Individual level Individual level Model: LPM Probit OLS Tobit OLS Tobit OLS Tobit Dependent variable: Punisher Punishment Mean punishment Median punishment (1) (2) (3) (4) (5) (6) (7) (8) Transfer − − − − − − − − − − − − − − − − − − − − − − − − − Table 5. Punishment and investment using individual-level data
Punishment Investment Risk-neutral and Risk-averse Risk-neutral and Risk-averse Mean p-value Median p-value Mean p-value Median p-value P [I0] 6.88 0.012 7.02 0.002 13.98 0.024 13.63 0.018 (6.89) (7.26) (16.44) (16.68) P&I0 1.86 1.36 24.05 24.20 (2.89) (2.59) (16.72) (17.02) Note: Mean and median refer to an average using mean and median individual-level data, respectively. Standard deviations are in parentheses. p-values are from the two-sided Wilcoxon rank-sum test. Table 6. Regression on investment (with risk-neutral and risk-averse)
Treatment: I0, P&I0 Level of data: Transfer level Transfer level Individual level Individual level Model: LPM Probit OLS Tobit OLS Tobit OLS Tobit Dependent variable: Investor Investment Mean investment Median investment (1) (2) (3) (4) (5) (6) (7) (8) Transfer 0.001 0.010* 0.072*** 0.117*** — — — — (0.001) (0.006) (0.026) (0.043) — — — — Treatment: P&I0 0.343*** 2.054*** 7.392* 14.578** 7.392 11.234* 7.742 14.924** (0.091) (0.594) (3.896) (5.819) (5.012) (5.709) (5.045) (6.349) Switching point 0.024 0.145 − − − − − − − − − − − − Table 7. The substitution effect (with risk-neutral and risk-averse)
Treatment: P&I0 I0
P&I0, I0 Level of data: Transfer level Transfer level Transfer level Model: OLS Tobit OLS Tobit OLS Tobit Dependent variable: Investment Investment Investment (conditional on a non-punisher) (1) (2) (3) (4) (5) (6) Transfer 0.079** 0.110** 0.064 0.132 0.060* 0.102** (0.032) (0.047) (0.045) (0.085) (0.032) (0.048) Treatment: P&I0 — — — — 7.313* 14.904** — — — — (3.741) (6.237) Switching point 2.554 4.753 − − − − − − − − − − Table 8. Punishment and investment using individual-level data
Punishment Investment Risk-neutral and Risk-aversion Risk-neutral and Risk-aversion Mean p-value Median p-value Mean p-value Median p-value P [Ineg] 6.88 0.019 7.02 0.003 6.12 0.131 4.86 0.080 (6.89) (7.26) (9.56) (9.16) P&Ineg 1.25 0.25 15.08 15.00 (2.12) (0.79) (19.20) (19.44) Note: Mean and Median refer to an average using mean and median individual-level data, respectively. Standard deviations are in parentheses. p-values are from the two-sided Wilcoxon rank-sum test. Figure 1. Punishment and investment in P, I0, and P&I0 treatments (with risk-neutral and risk-averse) a. Percentage of risk-neutral and risk-averse punishers c. Percentage of risk-neutral and risk-averse investors b. Expenditure for deduction points from risk-neutral and d. Expenditure for investment points from risk-neutral and risk-averse Player Cs risk-averse Player Cs Note: Bar=±1SE . . . . P e r c en t age o f pun i s he r s . . . P e r c en t age o f i n v e s t o r s E x pend i t u r e f o r dedu c t i on po i n t s E x pend i t u r e f o r i n v e s t m en t po i n t s Figure 2. Punishment and investment in P, Ineg and P&Ineg treatments (with risk-neutral and risk-averse) a. Percentage of risk-neutral and risk-averse punishers c. Percentage of risk-neutral and risk-averse investors b. Expenditure for deduction points from risk-neutral and d. Expenditure for investment points from risk-neutral risk-averse Player Cs risk-averse Player Cs Note: Bar=±1SE . . . . P e r c en t age o f pun i s he r s . . . . P e r c en t age o f i n v e s t o r s E x pend i t u r e f o r dedu c t i on po i n t s E x pend i t u r e f o r i n v e s t m en t po i n t s Supplementary Online Appendices for “ON THE FRAGILITY OF THIRD-PARTY PUNISHMENT: THE CONTEXT EFFECT OF A DOMINATED RISKY INVESTMENT OPTION” Appendix A. Instructions
These instructions are English translation. The instructions written in Korean were used in the experiment. The Korean instructions are available upon request.
A.1. General Instructions
The following instructions provide basic information for the experiment. Please read the instruction carefully and make your decision prudently for each task. You will participate in two tasks and join two distinct decision-making processes for each task. For convenience, we refer to the first task as Task 1 and the second task as Task 2. Specific instructions for Tasks 1 and 2 will be displayed on the monitor before starting each task. Your final payoff depends on your decisions determined in each task. If you have any questions about the instructions, please raise your hand quietly. An assistant will answer your question. Mobile phones and communication with other participants are not allowed during the experiment.
Payoff rules
Payoffs for each task will be displayed on the monitor after the entire experiment is completed. The unit of the payoff is “KRW (South Korean won)” for Task 1 and “token” for Task 2. Your final payoff for the experiment will be “[3000 KRW (show-up fee)] + [payoff in task 1] + [payoff in task 2] × 80 KRW.” At the end of the experiment, a questionnaire session will follow. The payment will be provided after the session. Specific instructions for Task 1 will be presented on the next screen. All subjects will participate identically in Task 1. After finish reading the instructions, click the OK button and wait for a moment.
A.2. Specific instructions for Task 1
The following are instructions for Task 1. In Task 1, ten questions are displayed as follows. Each question offers Lottery L and Lottery R. Select one lottery that you prefer for each question and click the OK button. Write L if you prefer Lottery L, and write R if you prefer Lottery R in the blank (You should write in capital letters). For instance, after all participants complete Tasks 1 and 2, your payoff for Task 1 will be realized by the decision determined in Task 1. In other words, one question in Task 1 will be selected by the computerized random procedure. Suppose that Question 1 is selected and you have chosen Lottery R for the given question. Then, the computer executes the lottery. Since Lottery R provides “8,000 KRW with probability 1/10 and 100 KRW with probability 9/10,” the computer randomly draws a ball in a basket containing ten balls composed of 1 “white” ball and 9 “red” balls. You will receive 8,000 KRW if a white ball is drawn and 100 KRW if a red ball is drawn. This will be your payoff for Task 1. A.3. Specific instructions for Task 2
The following are instructions for Task 2. In Task 2, three distinct types of Player have different roles (Players A, B, and C). Before Task 2 starts, the computer will randomly assign one Player type (Player A, B, or C) to each participant. Then, Players A, B, and C are randomly matched as a group. In Task 2, you make a decision using tokens. Your payoff in Task 2 is determined by decisions made by you and other participants in the same group. Your final payoff is informed after all participants complete making their decisions.
A.3.1. Player A
You are Player A. Your group has one Player B and one Player C. At the beginning of Task 2, you receive 100 tokens as an endowment. Also, Players B and C receive 0 token and 50 tokens, respectively.
Stage 1
In Stage 1, only Player A makes a decision. You, as Player A, decide how many tokens you would transfer to Player B from your own endowment. You can choose one of {0, 10, 20, 30, 40, 50} tokens for the transfer. Suppose that you transfer X token amount to Player B. Then, your endowment changes to
X tokens, and Player B’s endowment changes to X tokens in Stage 1. You can enter the transferred amount in the blank space appearing on the monitor.
Stage 2 [P treatment] In Stage 2, Player C can observe the token amount you transferred to Player B in Stage 1. In addition, Player C decides how many “deduction points” to impose on you. An explanation of deduction points is provided below. Suppose that Player C imposes Y number of deduction points on you. Then, Player C’s endowment is reduced by Y tokens, and your endowment is reduced by 3 times the Y tokens. Hence, one deduction point costs 1 token and reduces your token by 3. Moreover, Player C can freely assign tokens from 0 to 50 in integer unit for imposing deduction points. After all the participants have completed their own decision-making, you will be able to observe the token amount you transferred to Player B and the number of deduction points Player C imposed on you. Therefore, the final payoffs of each Player in Task 2 are Player A (You): (100 – [Token amount you transferred to Player B] – 3×[Deduction points]), Player B: ([Token amount you transferred to Player B]), and Player C: (50 – [Cost of imposed deduction points]).
Stage 2 [P&I0 treatment]
In Stage 2, Player C can observe the token amount you transferred to Player B in Stage 1. In addition, Player C decides how many “investment points” to purchase and how many “deduction points” to impose on you. Explanations of investment and deduction points are provided below. Suppose that Player C imposes Y number of deduction points on you. Then, Player C’s endowment is reduced by Y tokens and your endowment is reduced by 3 times the Y tokens. Hence, one deduction point costs 1 token and reduces your tokens by 3. Suppose that Player C purchases Z number of investment points. Then, Player C receives 2 times the Z tokens at half probability, or zero token at half probability. Hence, one investment point costs 1 token, and the investment profit is randomly determined. Note that the investment point does not affect your payoff. Moreover, Player C can freely assign tokens from 0 to 50 in integer unit for purchasing investment points and imposing deduction points. For instance, Player C can both purchase investment points and impose deduction points on you. Another option for Player C is to purchase investment points and impose no deduction point on you or purchase no investment points and impose deduction points on you. Lastly, Player C can purchase no investment point and impose no deduction point on you. However, for all cases, the total number of investment and deduction points should be between 0 and 50. After all participants have completed their own decision-making, you will be able to observe the token amount you transferred to Player B and the number of deduction points Player C imposed on you. Therefore, the final payoffs of each Player in Task 2 are Player A (You): 100 – [Token amount you transferred to Player B] – 3×[Deduction points], Player B: [Token amount you transferred to Player B], and Player C: 50 – [Cost of imposed deduction points] – [Cost of purchased investment points] + [Investment profit of Player C].
Stage 2 [I0 treatment]
In Stage 2, Player C can observe the token amount you transferred to Player B in Stage 1. In addition, Player C decides how many “investment points” to purchase. An explanation of investment points is provided below. Suppose that Player C purchases Z number of investment points. Then, Player C receives 2 times the Z tokens at half probability, or zero token at half probability. Hence, one investment point costs 1 token, and the investment profit is randomly determined. Note that the investment point does not affect your payoff. Moreover, Player C can freely assign tokens from 0 to 50 in integer unit for purchasing investment points. Therefore, the final payoffs of each Player in Task 2 are Player A (You): (100 – [Token amount you transferred to Player B]), Player B: ([Token amount you transferred to Player B]), and Player C: (50 – [Cost of purchased investment points] + [Investment profit of Player C]).
A.3.2. Player B
You are Player B. Your group has one Player A and one Player C. At the beginning of Task 2, you receive 0 token as an endowment. Also, Player A receives 100 tokens and Player C receives 50 tokens.
Stage 1
In Stage 1, only Player A makes a decision. Player A decides how many tokens to transfer to you from one’s endowment. Player A can choose one of {0, 10, 20, 30, 40, 50} tokens for the transfer. Suppose that Player A transfers X token amount to you. Then, Player A’s endowment changes to 100–X tokens, and your endowment changes to X tokens in Stage 1. First, we explain Player C’s role. Then, we explain your role in Task 2. Stage 2 [P treatment]
In Stage 2, Player C can observe the token amount Player A transferred to you in Stage 1. In addition, Player C decides how many “deduction points” to impose on Player A. An explanation of deduction points is provided below. Suppose that Player C imposes Y number of deduction points on Player A. Then Player C’s endowment is reduced by Y tokens and Player A’s endowment is reduced by 3 times Y tokens. Hence, one deduction point costs 1 token and reduces Player A’s tokens by 3. Moreover, Player C can freely assign tokens from 0 to 50 integer unit for imposing deduction points. Now, we explain your role in Task 2. Only Player A decides in Stage 1; hence, you immediately move on to Stage 2 for your decision-making. In Stage 2, you do not know Player A and C’s decisions. You write the “expected amount” of tokens Player A would transfer to you, that is, 0, 10, 20, 30, 40, or 50. In addition, you write the “expected amount” of deduction points Player C would impose on Player A. You should write the expected deduction points for each possible transfer level ({0, 10, 20, 30, 40, 50}). The maximum and minimum values for the expected deduction points are 0 and 50, respectively. Your expected values are irrelevant to your payoff. However, we would appreciate it if you would honestly write your expectations during the task. After all the participants have completed their own decision-making, you will be able to observe the token amount Player A transferred to you and the number of deduction points decided by Player C. Therefore, the final payoffs of each Player in Task 2 are Player A: (100 – [Token amount Player A transferred to you] – 3×[Deduction points]), Player B (You): ([Token amount Player A transferred to you]), and Player C: (50 – [Cost of imposed deduction points]).
Stage 2 [P&I0 treatment] In Stage 2, Player C can observe the token amount Player A transferred to you in Stage 1. In addition, Player C decides how many “investment points” to purchase and how many “deduction points” to impose on Player A. Explanations of investment and deduction points are provided below. Suppose that Player C imposes Y number of deduction points on Player A. Then Player C’s endowment is reduced by Y tokens, and Player A’s endowment is reduced by 3 times the Y tokens. Hence, one deduction point costs 1 token and reduces Player A’s tokens by 3. Suppose that Player C purchases Z number of investment points. Then, Player C receives 2 times the Z tokens at half probability or zero token at half probability. Hence, one investment point costs 1 token, and the investment profit is randomly determined. Note that the investment point does not affect Player A’s payoff. Moreover, Player C can freely assign tokens from 0 to 50 in integer unit for purchasing investment points and imposing deduction points. For instance, Player C can purchase investment points and impose deduction points on Player A. Another option for Player C is to purchase investment points and impose no deduction point on Player A or purchase no investment points and impose deduction points on Player A. Lastly, Player C can purchase no investment point and impose no deduction point on Player A. However, for all cases, the total number of investment and deduction points should be between 0 and 50. Now, we explain your role in Task 2. Since only Player A decides in Stage 1, you immediately move on to Stage 2 for your decision-making stage. In Stage 2, you do not know Player A and C’s decisions. You write the “expected amount” of tokens Player A would transfer to you, that is, 0, 10, 20, 30, 40, or 50. In addition, you write the “expected amount” of deduction points Player C would impose on Player A. You should write the expected deduction points for each possible transfer level {0, 10, 20, 30, 40, 50}. The maximum and minimum values for the expected deduction points are 0 and 50, respectively. Lastly, you write the “expected amount” of investment points Player C would purchase. You should write the expected investment points for each possible transfer level {0, 10, 20, 30, 40, 50}. The maximum and minimum values for the expected investment points are 0 and 50, respectively. Hence, for all cases, the total number of expected investment and deduction points should be between 0 and 50. Your expected values are irrelevant to your payoff. However, we would appreciate it if you would honestly write your expectations during the task. After all participants have completed their own decision-making, you will be able to observe the token amount Player A transferred to you and the number of deduction and investment points decided by Player C. Therefore, the final payoffs of each Player in Task 2 are Player A: (100 – [Token amount Player A transferred to you] – 3×[Deduction points]), Player B (You): ([Token amount Player A transferred to you]), and Player C: (50 – [Cost of imposed deduction points] – [Cost of purchased investment points] + [Investment profit of Player C]).
Stage 2 [I0 treatment]
In Stage 2, Player C can observe the token amount Player A transferred to you in Stage 1. In addition, Player C decides how many “investment points” to purchase. An explanation of investment points is provided below. Suppose that Player C purchases Z number of investment points. Then, Player C receives 2 times the Z tokens at half probability or zero token at half probability. Hence, one investment point costs 1 token, and the investment profit is randomly determined. Note that the investment point does not affect Player A’s payoff. Moreover, Player C can freely assign tokens from 0 to 50 in integer unit for purchasing investment points. Now, we explain your role in Task 2. Only Player A decides in Stage 1; hence, you immediately move on to Stage 2 for your decision-making. In Stage 2, you do not know Player A and C’s decisions. You write the “expected amount” of tokens Player A would transfer to you, that is, 0, 10, 20, 30, 40, or 50. In addition, you write the “expected amount” of investment points Player C would purchase. You should write the expected investment points for each possible transfer level ({0, 10, 20, 30, 40, 50}). The maximum and minimum values for the expected investment points are 0 and 50, respectively. Your expected values are irrelevant to your payoff. However, we would appreciate it if you would honestly write your expectations during the task. After all the participants have completed their own decision-making, you will be able to observe the token amount Player A transferred to you and the number of investment points decided by Player C. Therefore, the final payoffs of each Player in Task 2 are Player A: (100 – [Token amount Player A transferred to you]), Player B (You): ([Token amount Player A transferred to you]), and Player C: (50 – [Cost of purchased investment points] + [Investment profit of Player C]).
A.3.3. Player C
You are Player C. Your group has one Player A and one Player B. At the beginning of Task 2, you receive 50 tokens as an endowment. Also, Players A and B receive 100 tokens and 0 token, respectively.
Stage 1
In Stage 1, only Player A makes a decision. Player A decides how many tokens to transfer to Player B from his or her endowment. Player A can choose one of {0, 10, 20, 30, 40, 50} tokens for the transfer. Suppose that Player A transfers X token amount to Player B. Then, Player A’s endowment changes to
X tokens, and Player B’s endowment changes to X tokens in Stage 1. Now, we explain your role in Stage 2. Since only Player A decides in Stage 1, you immediately move on to Stage 2 for your decision-making.
Stage 2 [P treatment]
You, as Player C, decide how many “deduction points” to impose on Player A. An explanation of deduction points is provided below. Suppose that you impose Y number of deduction points on Player A. Then your endowment is reduced by Y tokens, and Player A’s endowment is reduced by 3 times the Y tokens. Hence, one deduction point costs 1 token and reduces Player A’s tokens by 3. Note that you must decide the token amount for imposing deduction points before you observe Player A’s actual transfer. Thus, you must write your decisions concerning each possible transfer level that Player A can choose. In other words, you can freely assign tokens from 0 to 50 in integer unit for imposing deduction points concerning Player A’s each possible transfer level, that is, 0, 10, 20, 30, 40, and 50. Hence, during your decision-making stage, a table of six possible cases ({0, 10, 20, 30, 40, 50}) will appear on the monitor. For each case, you can freely assign your tokens for deduction points. The token amount that remains after subtracting the costs of imposing deduction points from your initial endowment (50 tokens) becomes reserves in your private account. After all the participants have completed their own decision-making, you will be able to observe Player A’s actual transfer. Then, the corresponding deduction points you have determined during the decision-making stage will be realized. We call this the realized deduction points. Therefore, the final payoffs of each Player in Task 2 are Player A: (100 – [Token amount Player A transferred to Player B] – 3×[Realized deduction points]), Player B: ([Token amount Player A transferred to Player B]), and Player C (You): ([Realized private account]), that is, (50 – [Cost of realized deduction points]).
Stage 2 [P&I0 treatment]
You, as Player C, decide how many “investment points” to purchase and how many “deduction points” to impose on Player A. Explanations of investment and deduction points are provided below. Suppose that you impose Y number of deduction points on Player A. Then your endowment is reduced by Y tokens, and Player A’s endowment is reduced by 3 times the Y tokens. Hence, one deduction point costs 1 token and reduces Player A’s tokens by 3. Suppose that you purchase Z number of investment points. Then, you receive 2 times the Z tokens at half probability, or zero token at half probability. Hence, one investment point costs 1 token. Note that investment points do not affect Player A’s endowment. Your investment profit is determined by a computerized random procedure. Random procedure draws a “white ball” at half probability or a “red ball” at half probability. If you draw a white ball, you receive 2 times the Z tokens. If you draw a red ball, you receive nothing. Note that you must decide the token amount for purchasing investment points and imposing deduction points before you observe Player A’s actual transfer. Thus, you must write your decisions concerning each possible transfer level that Player A can choose. In other words, you can freely assign tokens from 0 to 50 in integer unit for purchasing investment points and imposing deduction points concerning each possible transfer level of Player A, that is, 0, 10, 20, 30, 40, and 50. Hence, during your decision-making stage, a table of six possible cases ({0, 10, 20, 30, 40, Player A: (100 – [Token amount Player A transferred to Player B] – 3×[Realized deduction points]), Player B: ([Token amount Player A transferred to Player B]), and Player C (You): ([Realized private account] + [Realized investment profit]), that is, if you draw a “white ball,” then (50 – [Cost of realized deduction points] – [Cost of realized investment points] + [Realized investment profit]), if you draw a “red ball,” then (50 – [Cost of realized deduction points] – [Cost of realized investment points]).
Stage 2 [I0 treatment]
You, as Player C, decide how many “investment points” to purchase. An explanation of investment points is provided below. Suppose that you purchase Z number of investment points. Then, you receive 2 times the Z tokens at half probability, or zero token at half probability. Hence, one investment point costs 1 token. Note that investment points do not affect Player A’s endowment. Your investment profit is determined by a computerized random procedure. Random procedure draws a “white ball” at half probability or a “red ball” at half probability. If you draw a white ball, you receive 2 times the Z tokens. If you draw a red ball, you receive nothing. Note that you must decide the token amount for purchasing investment points before you observe Player A’s actual transfer. Thus, you must write your decisions concerning each possible transfer level that Player A can choose. In other words, you can freely assign tokens from 0 to 50 in integer unit for purchasing investment points concerning each possible transfer level of Player A, that is, 0, 10, 20, 30, 40, and 50. Hence, during your decision-making stage, a table of six possible cases ({0, 10, 20, 30, 40, 50}) will appear on the monitor. You can purchase identical or different number of investment points for all six cases. The token amount that remains after subtracting the costs purchasing investment points from your initial endowment (50 tokens) becomes reserves in your private account. After all the participants have completed their own decision-making, you will be able to observe Player A’s actual transfer. Then, the corresponding investment points you have already determined during the decision-making stage will be realized. We call this as realized investment points. In addition, the outcome of the lottery is informed. Therefore, the final payoffs of each Player in Task 2 are Player A: (100 – [Token amount Player A transferred to Player B]), Player B: ([Token amount Player A transferred to Player B]), and Player C (You): ([Realized private account] + [Realized investment profit]), that is, if you draw a “white ball,” then (50 – [Cost of realized investment points] + [Realized investment profit]), if you draw a “red ball,” then (50 – [Cost of realized investment points]).
A.4. Examples of a controlled quiz [Player C in P&I0 treatment]
On the next screen, a simple quiz will be provided to help your understanding of Task 2. After reading the questions, write the correct answer. You can move on to the decision-making stage only if you write the correct answers to all the questions. If you incorrectly answer any question, you will not be able to move on to the next stage. In that case, please read the instructions again carefully and fix the incorrect answer(s). The result of the quiz is irrelevant to your payoff in the experiment.
1. Player A decided to transfer 10 tokens to Player B. Player C purchased 0 investment point and imposed 0 deduction point on player A when transferring 10 tokens to Player B. If you draw a “white ball,” what would be Player A, B, and C’s final tokens in Task 2, respectively? If you draw a “red ball,” what would be Player A, B, and C’s final tokens in Task 2, respectively? 2. Player A decided to transfer 10 tokens to Player B. Player C purchased 14 investment points and imposed 0 deduction point on Player A when transferring 10 tokens to Player B. (skip)
3. Player A decided to transfer 10 tokens to Player B. Player C purchased 0 investment point and imposed 18 deduction points on Player A when transferring 10 tokens to Player B. (skip)
4. Player A decided to transfer 10 tokens to Player B. Player C purchased 14 investment points and imposed 18 deduction points on Player A when transferring 10 tokens to Player B. (skip) A.5. Examples of Screenshots
The following are examples of screenshots for Player C in P&I0 treatment. The screenshots for the other players and the other treatments are similar besides the specific instructions for Task 2, the contents of quizzes, and the decisions to be made by Player C.
A.5.1. General instructions
A.5.2. Decision-making screen for Task 1 A.5.3. Task 2 i) Specific instruction for Player C in P&I0 treatment ii) Quiz and checking answers for Player C in P&I0 treatment iii) Decision-making procedure for Player C in P&I0 treatment iv) Task 2 payoff display for Player C in P&I0 treatment A.5.4. Payoff decision procedure for Task 1
A.5.5. Final total payoff display Appendix B. The normalized contextual concavity model
Suppose that there are two attributes: denote 𝐴𝐴 𝑀𝑀 as the material-payoff attribute and 𝐴𝐴 𝑃𝑃 as the psychological-payoff attribute. Let 𝑋𝑋 be the set of all alternatives, that is, 𝑋𝑋 = { 𝑇𝑇𝑇𝑇 , 𝐼𝐼 , 𝑆𝑆 } , where 𝑇𝑇𝑇𝑇 is the punishment option, 𝐼𝐼 is the investment option, and 𝑆𝑆 is the safe option. Note that the investment option yields the zero expected net return in P&I0 and I0 treatments, whereas it yields a strictly negative net return in P&Ineg and Ineg treatments. Let 𝑋𝑋 𝑟𝑟 ⊂ 𝑋𝑋 be the set of available alternatives under treatment 𝑟𝑟 ∈ { 𝑇𝑇 , 𝑇𝑇 & 𝐼𝐼 𝐼𝐼 𝑇𝑇 & 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 , 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 } . For instance, 𝑋𝑋 𝑃𝑃 ={ 𝑇𝑇𝑇𝑇 , 𝑆𝑆 } , 𝑋𝑋 𝐼𝐼0 = { 𝐼𝐼 , 𝑆𝑆 } , and 𝑋𝑋 𝑃𝑃 & 𝐼𝐼0 = {
𝑇𝑇𝑇𝑇 , 𝐼𝐼 , 𝑆𝑆 } . Denote 𝑡𝑡 as a transfer level from Player A to Player B, where 𝑡𝑡 ∈ {0, 10, 20, 30, 40, 50} . In this setting, the context where the third party faces will vary by the available options and by the transfer level. Each treatment offers different options; hence, a context is represented by ( 𝑟𝑟 , 𝑡𝑡 ) . The normalized contextual concavity model (NCCM) (Kivets et al., 2004) well describes how a compromise effect can affect a third party’s choice in our experiment. According to the model, individual 𝑖𝑖 ’s deterministic component of the utility of alternative 𝑗𝑗 in context ( 𝑟𝑟 , 𝑡𝑡 ) is equal to the sum of attribute terms that are concave functions of the normalized partworth gains in context ( 𝑟𝑟 , 𝑡𝑡 ) : 𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) = ��𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) � � 𝑊𝑊 𝑖𝑖 , 𝑗𝑗 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) � 𝑐𝑐 𝑘𝑘 𝑘𝑘 = ��𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) � 𝑘𝑘 �𝑊𝑊 𝑖𝑖 , 𝑗𝑗 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) � 𝑐𝑐 𝑘𝑘 𝑘𝑘 where 𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) is 𝑖𝑖 ’s deterministic component of the utility of alternative 𝑗𝑗 in context ( 𝑟𝑟 , 𝑡𝑡 ) , 𝑊𝑊 𝑖𝑖 , 𝑗𝑗 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) is 𝑖𝑖 ’s partworth of alternative 𝑗𝑗 with respect to attribute 𝑘𝑘 in context ( 𝑟𝑟 , 𝑡𝑡 ) , 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) and 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) are the maximum and minimum partworths, respectively, among available alternatives with respect to attribute 𝑘𝑘 in context ( 𝑟𝑟 , 𝑡𝑡 ) , and 𝑐𝑐 𝑘𝑘 ∈ (0, 1) is the concavity parameter of attribute 𝑘𝑘 . For example, 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 , ) is 𝑖𝑖 ’s (Player C) partworth of the punishment option ( 𝑇𝑇𝑇𝑇 ) with respect to the material-payoff attribute ( 𝐴𝐴 𝑀𝑀 ) when Player A transfers 10 tokens to Player B in P treatment ( 𝑇𝑇 , 10 ). Note that, in the second line of the equation, the first term, �𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) � 𝑘𝑘 , can substantially affect 𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) if 𝑐𝑐 𝑘𝑘 is close to . This implies that the deterministic component of the utility of the same alternative can differ depending on a given context. For instance, fixing attribute 𝑘𝑘 and transfer level 𝑡𝑡 , the difference between the maximum and minimum partworths ( 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑚𝑚𝑖𝑖𝑚𝑚 , 𝑘𝑘 ( 𝑟𝑟 , 𝑡𝑡 ) ) can be varied by treatment ( 𝑟𝑟 ) since each treatment has a different set of available alternatives. Fixing attribute 𝑘𝑘 and treatment 𝑟𝑟 , the difference between the maximum and minimum partworths can also be varied if the partworths fluctuate by transfer level ( 𝑡𝑡 ). The overall utility of alternative 𝑗𝑗 in context ( 𝑟𝑟 , 𝑡𝑡 ) consists of its deterministic component 𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) and an error term 𝜀𝜀 𝑖𝑖𝑗𝑗 . Specifically, assuming that 𝜀𝜀 𝑖𝑖𝑗𝑗 is i.i.d., the probability of 𝑖𝑖 choosing alternative 𝑗𝑗 in context ( 𝑟𝑟 , 𝑡𝑡 ) follows the multinomial logit model (McFadden, 1973): Pr 𝑖𝑖 �𝑗𝑗 |( 𝑟𝑟 , 𝑡𝑡 ) � = exp �𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) �∑ exp �𝑏𝑏𝑀𝑀 𝑖𝑖 , ℎ ( 𝑟𝑟 , 𝑡𝑡 ) � ℎ where 𝑏𝑏 is the logit scale parameter. Considering risk-neutral and risk-averse third parties, we assume the following: Assumption 1.
In terms of the material-payoff attribute, we assume that 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑟𝑟 , 𝑡𝑡 ) > 𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑀𝑀 ( 𝑟𝑟 , 𝑡𝑡 ) > 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑟𝑟 , 𝑡𝑡 ) for all ( 𝑟𝑟 , 𝑡𝑡 ) . Moreover, the partworths are constant for all ( 𝑟𝑟 , 𝑡𝑡 ) . Assumption 2.
In terms of the psychological-payoff attribute, we assume that 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) > 𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) > 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) for all ( 𝑟𝑟 , 𝑡𝑡 ) where 𝑡𝑡 = 0, 10, … , 40 . Moreover, when t is fixed, the partworths are constant for all 𝑟𝑟 . When 𝑟𝑟 is fixed, 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) and 𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) decrease in 𝑡𝑡 where 𝑡𝑡 = 0, 10, … , 40 . Assumption 1 is the partworth assumption for the material-payoff attribute. As discussed in Section 4 of the main text, such partworth inequalities exist because the risk-neutral and risk-averse evaluate the safe option the best, the investment option the second-best, and the costly punishment option the worst in terms of the material-payoff attribute. Also, we assume that the partworths are constant for all treatments and transfer levels. Assumption 2 is the partworth assumption for the psychological-payoff attribute. Likewise, such partworth inequalities exist because an individual evaluates the punishment option the best, the investment option the second-best, and the safe option the worst in terms of the psychological-payoff attribute. Here, we assume that the partworths are constant across all treatments given any unequal transfer. For instance, 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) = 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) for all 𝑡𝑡 = 0, 10, … , 40 . However, the partworths are allowed to fluctuate depending on unequal transfer levels given any treatment. In particular, decreasing 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) and 𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑟𝑟 , 𝑡𝑡 ) in 𝑡𝑡 implies that negative emotions such as anger are alleviated as Player C observes more fair allocation determined by Player A. Given Assumptions 1 and 2, we can now attain 𝑀𝑀 𝑖𝑖 , 𝑗𝑗 ( 𝑟𝑟 , 𝑡𝑡 ) for each alternative in each context. Throughout the following analysis, we focus on P&I0, P, and I0 treatments , and 𝑡𝑡 ∈ {0, … , 40} . In P&I0 treatment, we have 𝑋𝑋 𝑃𝑃 & 𝐼𝐼0 = {
𝑇𝑇𝑇𝑇 , 𝐼𝐼 , 𝑆𝑆 } . Thus, we obtain 𝑀𝑀 𝑖𝑖 , 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � , 𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � 𝑀𝑀 �𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � 𝑐𝑐 𝑀𝑀 + �𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � 𝑃𝑃 �𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � 𝑐𝑐 𝑃𝑃 , 𝑀𝑀 𝑖𝑖 , 𝑆𝑆 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � . In 𝑇𝑇 treatment, we have 𝑋𝑋 𝑃𝑃 = { 𝑇𝑇𝑇𝑇 , 𝑆𝑆 } . Thus, we obtain 𝑀𝑀 𝑖𝑖 , 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) � , 𝑀𝑀 𝑖𝑖 , 𝑆𝑆 ( 𝑃𝑃 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 , 𝑡𝑡 ) � . In 𝐼𝐼 treatment, we have 𝑋𝑋 𝐼𝐼0 = { 𝐼𝐼 , 𝑆𝑆 } . Thus, we obtain 𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝐼𝐼0 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑃𝑃 ( 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝐼𝐼0 , 𝑡𝑡 ) � , 𝑀𝑀 𝑖𝑖 , 𝑆𝑆 ( 𝐼𝐼0 , 𝑡𝑡 ) = �𝑊𝑊 𝑖𝑖 , 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑖𝑖 , 𝐼𝐼 , 𝐴𝐴 𝑀𝑀 ( 𝐼𝐼0 , 𝑡𝑡 ) � . We now present the first proposition implying the decrease in the probability of choosing the punishment option when the investment option is additionally available.
Proposition 1.
The probability of choosing option
𝑇𝑇𝑇𝑇 in P&I0 [P&Ineg] treatment is lower than We can obtain an analogous analysis using P&Ineg and Ineg treatments. the probability of choosing option 𝑇𝑇𝑇𝑇 in P treatment. [Proof of Proposition 1] For simplicity, we suppress the subscript 𝑖𝑖 . Note that for any 𝑏𝑏 ∈ (0, 1) and 𝑡𝑡 ∈ {0, … , 40} , the probability of choosing alternative 𝑇𝑇𝑇𝑇 in P&I0 treatment is Pr �𝑇𝑇𝑇𝑇 |( 𝑇𝑇 & 𝐼𝐼 𝑡𝑡 ) � = exp�𝑏𝑏𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �exp�𝑏𝑏𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝑆𝑆 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � , and the probability of choosing alternative 𝑇𝑇𝑇𝑇 in P treatment is Pr �𝑇𝑇𝑇𝑇 |( 𝑇𝑇 , 𝑡𝑡 ) � = exp�𝑏𝑏𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) �exp�𝑏𝑏𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝑆𝑆 ( 𝑃𝑃 , 𝑡𝑡 ) � . By Assumptions 1 and 2, we have 𝑊𝑊 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = 𝑊𝑊 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) − 𝑊𝑊 𝑆𝑆 , 𝐴𝐴 𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) > 0 and 𝑊𝑊 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) − 𝑊𝑊 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = 𝑊𝑊 𝑆𝑆 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 , 𝑡𝑡 ) − 𝑊𝑊 𝑇𝑇𝑃𝑃 , 𝐴𝐴 𝑀𝑀 ( 𝑃𝑃 , 𝑡𝑡 ) > 0 , respectively. Then, we obtain 𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = 𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 , 𝑡𝑡 ) and 𝑀𝑀 𝑆𝑆 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) = 𝑀𝑀 𝑆𝑆 ( 𝑃𝑃 , 𝑡𝑡 ) . Since 𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) is strictly positive for all 𝑡𝑡 = 0, … , 40 , it follows that Pr �𝑇𝑇𝑇𝑇 |( 𝑇𝑇 & 𝐼𝐼 𝑡𝑡 ) �
For any 𝑏𝑏 ∈ (0, 1) and for any 𝑡𝑡 = 0, 10, … , 40 , we assume that exp �𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) + 𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝑆𝑆 ( 𝐼𝐼0 , 𝑡𝑡 ) � > exp �𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝐼𝐼0 , 𝑡𝑡 ) + 𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � + exp �𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝐼𝐼0 , 𝑡𝑡 ) + 𝑏𝑏𝑀𝑀 𝑖𝑖 , 𝑆𝑆 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � . The main implication of Assumption 3 is that the deterministic component of the utility of option 𝐼𝐼 in P&I0 treatment, 𝑀𝑀 𝑖𝑖 , 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) , is sufficiently large. With the additional assumption, we can present the second proposition implying the increase in the probability of choosing the investment option when the punishment option is additionally available. Proposition 2.
The probability of choosing option 𝐼𝐼 in P&I0 [P&Ineg] treatment is higher than the probability of choosing option 𝐼𝐼 in I0 [Ineg] treatment. [Proof of Proposition 2] For any 𝑏𝑏 ∈ (0, 1) and 𝑡𝑡 ∈ {0, … , 40} , the probability of choosing option 𝐼𝐼 is Pr �𝐼𝐼 |( 𝑇𝑇 & 𝐼𝐼 𝑡𝑡 ) � = exp�𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �exp�𝑏𝑏𝑀𝑀 𝑇𝑇𝑃𝑃 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝑆𝑆 ( 𝑃𝑃 & 𝐼𝐼0 , 𝑡𝑡 ) � , and Pr �𝐼𝐼 |( 𝐼𝐼 𝑡𝑡 ) � = exp�𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝐼𝐼0 , 𝑡𝑡 ) �exp�𝑏𝑏𝑀𝑀 𝐼𝐼 ( 𝐼𝐼0 , 𝑡𝑡 ) �+exp�𝑏𝑏𝑀𝑀 𝑆𝑆 ( 𝐼𝐼0 , 𝑡𝑡 ) � in P&I0 and I0 treatments, respectively. Then, by Assumption 3, we have Pr �𝐼𝐼 |( 𝑇𝑇 & 𝐼𝐼 𝑡𝑡 ) � > Pr �𝐼𝐼 |( 𝐼𝐼 𝑡𝑡 ) � for all unequal allocations. To sum up, Propositions 1 and 2 show that when all three options are available, the probability of investing increases, whereas the probability of punishing decreases. This indicates that the investment option works as a compromise. Therefore, we construct the following hypotheses based on these results: Hypothesis 1.
For the risk-neutral and the risk-averse, the choice frequency and the expenditure of punishment in P&I0 [P&Ineg] treatment are lesser than those in P treatment.
Hypothesis 2.
For the risk-neutral and the risk-averse, the choice frequency and the expenditure of investment in P&I0 [P&Ineg] treatment are greater than those in I0 [Ineg] treatment. References for Appendix B
Kivetz, R., Netzer, O., Srinivasan, V. (2004). Alternative models for capturing the compromise effect.
Journal of Marketing Research , (3), 237–257. McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics , Paul Zarembka, ed. New York: Academic Press, 105–142. Appendix C. Robustness check for the third party’s behavior
C.1. Risk-consistent third parties in P, P&I0, and I0 treatments
In Section 5.1 of the main text, we have shown that TPP is fragile in the presence of an unattractive investment option where the expected net return equals zero. In addition, the findings from Section 5.2 indicate that Player C is likely to, or at least not decrease the amount of, investment in the unattractive lottery if TPP is available simultaneously. This tendency appears even though we consider all risk-consistent third parties. Figures C1a and C1b show that at unequal allocations, risk-consistent Player C is less likely to punish Player A when the investment option was also available compared with a circumstance when the punishment option was solely available. Using a chi-square test, we find that the percentage of punishers are significantly smaller in P treatment than in P&I0 treatment for some unequal transfer levels (all p<0.076 at transfer levels 0–30). Likewise, employing a two-sided Wilcoxon rank-sum test, we find that the expenditures for deduction points are significantly lower in P treatment than in P&I0 treatment for some unequal transfer levels (all p<0.033 at transfer levels 0–30). Furthermore, we examine a third party’s punishing behavior using the individual-level data as presented in Table C1. The averages of mean [median] punishment are 7.54 [7.28] in P treatment and 3.23 [2.83] in P&I0 treatment, and the difference is statistically significant (p=0.023 [p=0.005], two-sided Wilcoxon rank-sum test). One may argue that considering all the risk-consistent parties, the diminished demand for TPP can be attributed to risk-loving third parties. Specifically, in P&I0 treatment, a risk-loving punisher’s problem is deciding how many tokens one will allocate to deduction and investment points within one’s budget constraint. Due to the constraint, the risk-loving may decrease the punishment expenditure and increase the investment expenditure. Hence, if risk-loving third parties are greater in P&I0 treatment than in P treatment, then the diminished demand for TPP could occur without the treatment effect. However, we find no strong evidence that the distribution of Player C’s risk attitude is heterogeneous between the treatments. The averages of Player C’s
Switching point are 6.00 and 5.81 in P and P&I0 treatments, respectively, and the difference is insignificant (p>0.742, two-sided Wilcoxon rank-sum test). This implies the nonheterogeneity of distribution of Player C’s risk attitude between the treatments. Figures C1c and C1d show that risk-consistent Player C is more likely to invest in the lottery in P&I0 treatment than in I0 treatment. For each transfer level, the difference in investment proportions is statistically significant (all p<0.016 at transfer levels 0–50, chi-square test), and the difference in investment expenditures is significantly different (all p<0.070 at transfer levels 0–50, two-sided Wilcoxon rank-sum test). Using the individual-level data as described in Table C1, we obtain 15.41 [15.18] and 24.15 [24.38] as the averages of mean [median] investment in I0 treatment and P&I0 treatment, respectively, and the difference is statistically significant (p=0.046 [p=0.032], two-sided Wilcoxon rank-sum test). Likewise, the increased demand for investment can be caused by the biased selection of Player C in terms of risk attitude. For instance, when risk-loving third parties are greater in P&I0 treatment than in I0 treatment, then the increased demand we observed above could happen regardless of the treatment effect. However, the distributions of Player C’s risk attitude between P&I0 and I0 treatments do not seem to be heterogeneous. Hence, we conclude that similar punishment and investment behaviors are observed even if we consider the entire risk-consistent third parties.
Table C1. Punishment and investment using the individual-level data
Punishment Investment Risk-consistent Risk-consistent Mean p-value Median p-value
Mean p-value Median p-value P [I0] 7.54 0.023 7.28 0.005 15.41 0.046 15.18 0.032 (7.13) (7.01) (15.84) (16.17) P&I0 3.23 2.83 24.15 24.38 (5.99) (6.09) (16.50) (16.78) Note: Mean and median refers to an average using mean and median individual-level data, respectively. Standard deviations are in parentheses. p-values are from the two-sided Wilcoxon rank-sum test. The averages of Player C’s
Switching point are 6.23 and 5.81 in I0 and P&I0 treatments, respectively, and the difference is not statistically significant (p>0.404, two-sided Wilcoxon rank-sum test). This implies the nonheterogeneity of distribution of Player C’s risk attitude between the treatments. In addition, for risk-loving Player Cs, the averages of investment are 24.44 (n=3) in I0 treatment and 24.75 (n=4) in P&I0 treatment. Although we cannot conduct any statistical test due to the small sample size, the difference is not large. Figure C1. Punishment and investment in P, I0, and P&I0 treatments (with risk-consistent) a. Percentage of risk-consistent punishers c. Percentage of risk-consistent investors b. Expenditure for deduction points from risk-consistent d. Expenditure for investment points from risk-consistent Player Cs Player Cs Note: Bar= ± . . . . P e r c en t age o f pun i s he r s . . . . . P e r c en t age o f i n v e s t o r s E x pend i t u r e f o r dedu c t i on po i n t s E x pend i t u r e f o r i n v e s t m en t po i n t s C.2. Risk-neutral and risk-averse third parties in P, P&I0, and I0 treatments
In the main text, we examine a third party’s behavior using regression methods. Note that these results are robust even if we consider the
Interaction term, which is the product of
Transfer and
Treatment , as an independent variable in the models. Analysis of punishing behavior considering the risk-neutral and the risk-averse is illustrated in Section 5.1, and related regression results are reported in Table 4 in the main text. Following the models in the text, we regress
Punisher or Punishment on Transfer , Treatment , Interaction , and other controlling variables using LPM, Probit, OLS, and Tobit methods. The regression results are presented in columns 1–4 in Table C2. All
Treatment variables indicate negative coefficients, and they are significantly different from zero. Therefore, the
Interaction term does not qualitatively affect the regression results implying the diminished demand for punishment. Meanwhile, the analysis of investment behavior considering the risk-neutral and the risk-averse is illustrated in Section 5.2, and related regression results are provided in Table 6. Likewise, for further analysis, we regress
Investor or Investment on Transfer , Treatment , Interaction , and other controlling variables using LPM, Probit, OLS, and Tobit methods. The results are reported in columns 5–8 in Table C2, and they show that the coefficients of
Treatment are all positive and significantly different from zero. Hence, we confirm that the regression results implying the increased demand for investment are robust even if we consider the
Interaction term in the models as well. Note that in column 3 in Table C2, the coefficient of
Interaction is positive and significant. This indicates that when an OLS but not a Tobit method is used, the marginal effect of
Transfer on Punishment is smaller in P&I0 treatment than in P treatment. The different results between the two methods may be due to truncated data. Indeed, the Tobit model in column 4 considers 176 left-censored and 1 right-censored data. Note that in Table C2, the
Interaction term is omitted in column 6 because all Player Cs chose to invest on the lottery at the transfer levels 10–50 in P&I0 treatment. Table C2. Regression on punishment and investment (with risk-neutral and risk-averse)
Treatment: P, P&I0 I0, P&I0 Level of data: Transfer level Transfer level Model: LPM Probit OLS Tobit LPM Probit OLS Tobit Dependent variable: Punisher Punishment Investor Investment (1) (2) (3) (4) (5) (6) (7) (8) Transfer − − − − − − − − − − − − − − − − − − − − − C.3. Risk-averse third parties in P, P&I0, and I0 treatments
As discussed in Sections 4 and 5, punishing and investing behaviors only considering risk-averse third parties are worthy to examine since some risk-neutral third parties may not consider the investment option as a compromise. Figures C2a and C2b show that risk-averse Player C is still reluctant to punish Player A in P&I0 treatment than in P treatment. Both the proportion of punishers and punishment expenditures are significantly lower in P&I0 treatment than in P treatment for almost all unfair transfer levels (all p<0.072 at transfer levels 10–40, chi-square test; all p<0.093 at transfer levels 0–40, two-sided Wilcoxon rank-sum tests). Moreover, as presented in Table C3, the averages of mean [median] punishment are 6.47 [6.16] and 1.35 [0.77] in P and P&I0 treatments, respectively, and the difference is statistically significant (p=0.058 [p=0.015], two-sided Wilcoxon rank-sum tests). All columns in Table C4 and columns 1–4 in Table C6 report related regression results. Note that all coefficients of
Treatment have negative values and are significantly different from zero. Therefore, the diminished demand for TPP holds even when we only consider risk-averse third parties. Next, we examine the investing behavior of risk-averse third parties. Figure C2c shows that for each transfer level, the proportion of investors is significantly higher in P&I0 treatment than in I0 treatment (all p<0.056 at transfer level 0–50, chi-square test). This implies the apparent effect of the punishment opportunity in P&I0 treatment on the investment behavior of risk-averse Player Cs. Figure C2d shows that although the differences are insignificant, the investment expenditure is higher in P&I0 treatment than in I0 treatment at all transfer levels. Similarly, as shown in Table C3, the averages of mean [median] investments are 14.06 [13.88] and 20.97 [21.23] in I0 and P&I0 treatments, respectively. Although the differences are statistically insignificant, we can still confirm that the demand for investment in P&I0 treatment is at least not smaller than the investment demand in I0 treatment. The related regression results are presented in all columns in Table C5 and columns 5–8 in Table C6. Likewise, the coefficients of
Treatment indicate positive values, and a few of them are significantly different from zero. Hence, the results considering The coefficient of
Interaction is positive and significant in column 6 in Table C4. This indicates that when an OLS but not a Tobit method is used, the marginal effect of
Transfer on Punishment is smaller in P&I0 treatment than that in P treatment. The different results between the two methods may be due to truncated data. Indeed, the Tobit model used in columns 7 and 8 considers 122 left-censored and 1 right-censored data. We omit the regression results of Probit models in columns 3 and 4 in Table C5 since the convergence is not achieved. only the risk-averse weakly support the increased demand for investment when both punishing and investing options are available. Table C3. Punishment and investment using the individual-level data
Punishment Investment Risk-aversion Risk-aversion Mean p-value Median p-value
Mean p-value Median p-value P [I0] 6.47 0.058 6.16 0.015 14.06 0.299 13.88 0.247 (7.20) (6.96) (13.77) (13.89) P&I0 1.35 0.77 20.97 21.23 (2.58) (1.88) (16.97) (17.16) Note: Mean and median refer to an average using mean and median individual-level data, respectively. Standard deviations are in parentheses. p-values are from the two-sided Wilcoxon rank-sum test.
The failure of the convergence is due to failure of the identification for Probit in P&I0 treatment, where all subjects choose to invest for all transfer level. Figure C2. Punishment and Investment in P, I0 and P&I0 treatments (with risk-averse) a. Percentage of risk-averse punishers c. Percentage of risk-averse investors b. Expenditure for deduction points from risk-averse d. Expenditure for investment points from risk-averse Player Cs Player Cs Note: Bar= ± . . . . P e r c en t age o f pun i s he r s . . . . . P e r c en t age o f i n v e s t o r s E x pend i t u r e f o r dedu c t i on po i n t s E x pend i t u r e f o r i n v e s t m en t po i n t s Table C4: Regression on punishment (with risk-averse)
Treatment: P, P&I0 Level of data: Transfer level Transfer level Model: LPM Probit OLS Tobit Dependent variable: Punisher Punisher Punishment Punishment (1) (2) (3) (4) (5) (6) (7) (8) Transfer − − − − − − − − − − − − − − − − − − − − − − − − − − − − Table C5: Regression on investment (with risk-averse)
Treatment: I0, P&I0 Level of data: Transfer level Transfer level Model: LPM Probit OLS Tobit Dependent variable: Investor Investor Investment Investment (1) (2) (3) (4) (5) (6) (7) (8) Transfer 0.000 0.000 - - 0.039 0.020 0.053 0.031 (0.001) (0.002) - - (0.031) (0.049) (0.040) (0.068) Treatment: P&I0 0.274* 0.280* - - 5.595 4.666 11.017 10.016 (0.134) (0.141) - - (4.877) (4.953) (6.786) (6.724) Interaction: Transfer × Treatment - 0.000 - - - 0.037 - 0.040 - (0.002) - - - (0.062) - (0.082) Switching point − − − − − − − − − − - - Table C6: Regression on punishment and investment (with risk-averse)
Treatment: Level of data: Individual level Individual level Individual level Individual level Model: OLS Tobit OLS Tobit OLS Tobit OLS Tobit Dependent variable: Mean punishment Median punishment Mean investment Median investment (1) (2) (3) (4) (5) (6) (7) (8) Treatment: P&I0 − − − − − − − − − − − − − − − − − − − C.4. Risk-neutral and risk-averse third parties in P, P&Ineg, and Ineg treatments
For the extended analysis in the main text, we examine a third party’s behavior using the supplementary treatments, namely, P&Ineg and Ineg treatments. In this subsection, we provide related regression results of the supplementary treatments and confirm the consistency of these results with the main findings. Consider risk-neutral and risk-averse third parties. First, we regress
Punisher or Punishment on Transfer,
Treatment , Interaction , and other controlling variables. Here,
Treatment is defined as 0 if P treatment and 1 if P&Ineg treatment. The regression results of
Punisher are reported in columns 1–4 in Table C7, whereas the results of
Punishment are reported in columns 5–8 in Table C7. In accordance with the findings in the main text, all
Treatment variables indicate negative coefficients and are significantly different from zero. In addition, we regress
Punishment on Treatment and other controlling variables using the individual-level data. The results are presented in Table C9. Consistently,
Treatment variables indicate negative values and are significantly different from zero. Next, we regress
Investor or Investment on Transfer,
Treatment , Interaction , and other controlling variables. Here,
Treatment is defined as 0 if Ineg treatment and 1 if P&Ineg treatment. The results of
Investor are presented in columns 1–4 in Table C8, whereas the results of
Investment are presented in columns 5–8 in Table C8. We find that all
Treatment variables indicate positive coefficients and are significantly different from zero. Moreover, we regress
Investment on Treatment and other controlling variables using the individual-level data. The results are presented in Table C9. Consistent with the findings from the transfer level data, all
Treatment variables are positive and significantly different from zero. Therefore, the results in P&Ineg, Ineg and P treatments confirm the robustness of the findings in P&I0, I0 and P treatments in the main text. Note that the significance of coefficients of
Interaction is different between the OLS method and Tobit method as displayed in columns 6 and 8, respectively, in Table C7. This may be due to truncated data where a Tobit method, in column 8, considers 125 left-censored and 1 right-censored data. Table C7: Regression on punishment (with risk-neutral and risk-averse)
Treatment: P, P&Ineg Level of data: Transfer level Transfer level Model: LPM Probit OLS Tobit Dependent variable: Punisher Punisher Punishment Punishment (1) (2) (3) (4) (5) (6) (7) (8) Transfer − − − − − − − − − − − − − − − − − − − − − Table C8: Regression on investment (with risk-neutral and risk-averse)
Treatment: Ineg, P&Ineg Level of data: Transfer level Transfer level Model: LPM Probit OLS Tobit Dependent variable: Investor Investor Investment Investment (1) (2) (3) (4) (5) (6) (7) (8) Transfer 0.000 − − − − − − − − − − − − − Table C9: Regression on punishment and investment (with risk-neutral and risk-averse)
Treatment: P, P&Ineg Ineg, P&Ineg Level of data: Individual level Individual level Model: OLS Tobit OLS Tobit OLS Tobit OLS Tobit Dependent variable: Mean punishment Median punishment Mean investment Median investment (1) (2) (3) (4) (5) (6) (7) (8) Treatment: P&Ineg − − − − − − − − − − C.5. Substitution effect between the punishment and the investment options
In the main text, we have suggested that investment option may work as a compromise by showing the possible substitution effect between the punishment option and the investment option. One way to verify the substitution effect is to compare the extent of investment conditional on a non-punisher in P&I0 treatment to the extent of investment in I0 treatment. In this subsection, we verify that the substitution effect we claim is indeed robust even if the
Interaction term is included as an independent variable in the regression models. Furthermore, the claim is also supported by the regression results from the supplementary treatments with other controlled variables. In Table C10, the additional regression results from I0 and P&I0 treatments are reported in columns 1 and 2, whereas those from Ineg and P&Ineg treatments are reported in columns 3–6. Note that all
Treatment variables have positive values and are significantly different from zero. This supports our claim about the substitution effect and the hypothesis about the compromise effect. Table C10: The substitution effect (with risk-neutral and risk-averse)
Treatments I0, P&I0 Ineg, P&Ineg Level of data: Transfer level Transfer level Model: OLS Tobit OLS Tobit Dependent variable: Investment Investment Investment Investment (conditional on a non-punisher) (conditional on a non-punisher) (1) (2) (3) (4) (5) (6) Transfer 0.064 0.123 − − − − − − − − − − − − − − Appendix D. Dictator’s actual transfer
We examine Player A’s transfer behavior based on P, P&I0, and I0 treatments. Throughout this section, we consider only risk-consistent Player A. However, the overall results are not qualitatively affected even though the entire data set is considered. Roughly, 58% (n=26), 67% (n=24), and 39% (n=23) of Player A transferred a positive token amount to Player B in P, P&I0, and I0 treatments, respectively. The difference in transfer percentages between P and P&I0 treatments is insignificant (p>0.513, chi-square test), whereas the difference between P&I0 and I0 treatments is significant (p=0.059, chi-square test). Player A transferred about 20, 18, and 10 tokens, on average, to Player B in P, P&I0, and I0 treatments, respectively. Likewise, the difference in transferred tokens between P and P&I0 treatments is insignificant (p>0.848, two-sided Wilcoxon rank-sum test), whereas the difference between P&I0 and I0 treatments is significant (p=0.086, two-sided Wilcoxon rank-sum test). These results suggest that Player A felt threatened by the sanctioning mechanism, which might have led one to increase the transfer to avoid Player C’s punishment. For further analysis, we regress
Transfer Dummy and
Transfer Level on Treatment and other controlling variables.
Transfer Dummy is defined as 0 if Player A transferred nothing, and 1 if Player A transferred any positive token amount to Player B.
Transfer Level is defined as the token amount Player A transferred to Player B. The results comparing P and P&I0 treatments are reported in columns 1–4 in Table D1. As the above tests demonstrated, the coefficients of the
Treatment variables indicate inconsistent signs across models, and they are even insignificant. The results comparing I0 and P&I0 treatments are reported in columns 5–8 in Table D1. Consistent with the above tests, the
Treatment variables indicate positive coefficients although they are marginally insignificant besides Probit (all p<0.152 in columns 5–8). These results imply that Player A is willing to allocate more tokens to Player B when Player C had a punishing opportunity. Therefore, the sanctioning mechanism may have affected Player A’s behavior to transfer more tokens to Player B, whereas the investment mechanism did not. Focusing on the coefficients of
Treatment in Table D1 in columns 5 –
8, if we exclude independent variables related to personality traits in the models, the p-values become more significant. These suggest that not only the threat of punishment but also personality traits may have played a crucial role in Player A’s transfer behavior. Table D1. Player A's actual transfer (with risk-consistent)
Treatments P, P&I0 I0, P&I0 Model: LPM Probit
OLS
Tobit LPM Probit
OLS
Tobit Dependent variable: Transfer Dummy Transfer Level Transfer Dummy Transfer Level (1) (2) (3) (4) (5) (6) (7) (8) Treatment: P&I0 0.020 0.170 − − − − − − − − − − − − − − − − −0.226 0.205 0.330 0.074 Note: The dependent variable in Tobit models is truncated at 0 (left-censored) and 50 (right-censored). Socio-demographic includes gender, income, and Economics major. Standard errors are in parentheses. ***, **, and * denote significance at 1%, 5%, and 10% levels, respectively.