Eva M. Krockow

Social Value Induction and Cooperation in the Centipede Game

The Centipede game provides a dynamic model of cooperation and competition in repeated dyadic interactions. Two experiments investigated psychological factors driving cooperation in 20 rounds of a Centipede game with significant monetary incentives and anonymous and random re-pairing of players after every round. The main purpose of the research was to determine whether the pattern of strategic choices observed when no specific social value orientation is experimentally induced—the standard condition in all previous investigations of behavior in the Centipede and most other experimental games—is essentially individualistic, the orthodox game-theoretic assumption being that players are individualistically motivated in the absence of any specific motivational induction. Participants in whom no specific state social value orientation was induced exhibited moderately non-cooperative play that differed significantly from the pattern found when an individualistic orientation was induced. In both experiments, the neutral treatment condition, in which no orientation was induced, elicited competitive behavior resembling behavior in the condition in which a competitive orientation was explicitly induced. Trait social value orientation, measured with a questionnaire, influenced cooperation differently depending on the experimentally induced state social value orientation. Cooperative trait social value orientation was a significant predictor of cooperation and, to a lesser degree, experimentally induced competitive orientation was a significant predictor of non-cooperation. The experimental results imply that the standard assumption of individualistic motivation in experimental games may not be valid, and that the results of such investigations need to take into account the possibility that players are competitively motivated.

Competitive centipede games: Zero-end payoffs and payoff inequality deter reciprocal cooperation

Reciprocal cooperation can be studied in the Centipede game, in which two players alternate in choosing between a cooperative GO move and a non-cooperative STOP move. GO sustains the interaction and increases the player pair’s total payoff while incurring a small personal cost; STOP terminates the interaction with a favorable payoff to the defector. We investigated cooperation in four Centipede games differing in their payoffs at the game’s end (positive versus zero) and payoff difference between players (moderate versus high difference). The games shared the same game-theoretic solution, therefore they should have elicited identical decision patterns, according to orthodox game theory. Nevertheless, both zero-end payoffs and high payoff inequality were found to reduce cooperation significantly. Contrary to previous predictions, combining these two factors in one game resulted in a slight weakening of their independent deterrent effects. These findings show that small changes in the payoff function have large and significant effects on cooperation, and that the effects do not combine synergistically.

Reasons for Cooperating in Repeated Interactions: Social Value Orientations, Fuzzy Traces, Reciprocity, and Activity Bias

Many human interactions involve patterns of turn-taking cooperation that can be modeled by the deeply paradoxical Centipede game. A backward induction argument suggests that cooperation is irrational in such interactions, but experiments have demonstrated that players cooperate frequently and earn better payoffs as a consequence. We formulate 6 competing theories of cooperation in Centipede games and report the results of 2 experiments, based on investigations of several closely matched games with different payoff structures and different methods of reaching decisions. The results show that turn-taking cooperation does not appear to be explained by reciprocity theory, activity bias theory, or a motive to maximize relative payoffs, but that collective rationality, in the form of a motive to maximize joint payoffs, and fuzzy-trace theory can explain cooperation in interactions of this type. Reciprocity increases cooperation across repeated games between fixed player pairs, but there is no evidence of reciprocity influencing cooperation within games.

Cooperation in repeated interactions: A systematic review of Centipede game experiments, 1992–2016

ABSTRACT Cooperation is a fundamental form of social interaction, and turn-taking reciprocity one of its most familiar manifestations. The Centipede game provides a formal model of such alternating reciprocal cooperation, but a backward induction (BI) argument appears to prove logically that instrumentally rational players would never cooperate in this way. A systematic review of experimental research reveals that human decision makers cooperate frequently in this game, except under certain extreme conditions. Several game, situational, and individual difference variables have been investigated for their influence on cooperation. The most influential are aspects of the payoff function (especially the social gain from cooperation and the risk associated with a cooperative move), the number of players, repetitions of the game, group vs. individual decisions, and players’ social value orientations (SVOs). Our review of experimental evidence suggests that other-regarding preferences, including prosocial behavioural dispositions and collective rationality, provide the most powerful explanation for cooperation.

Cooperation and Trust in Japanese and British Samples: Evidence from Incomplete Information Games

Most human relationships are characterized by reciprocal patterns of give-and-take that can be studied using a decision-making task called the Centipede game. The game involves 2 players alternating in choosing between cooperation and defection, with their choices affecting payoffs to themselves and the co-player. We compared trust and cooperation of Japanese and U.K. samples in the Centipede game. To increase the game’s applicability to real-life decision situations, we added 3 treatment conditions to manipulate payoff information. Our between-subjects design comprised the following 4 conditions: (a) full payoff information, (b) full payoff information framed as percentages, (c) partial payoff information with absolute (own payoff) information only, and (d) partial payoff information with relative information only. Comparing Japanese and U.K. students’ decisions, the Japanese cooperated significantly more frequently than the British. The manipulation of payoff information also affected decision making. In Japan, both treatment conditions with incomplete information yielded significantly higher cooperation levels than the control. In the U.K., only the condition with absolute payoff information produced significantly higher cooperativeness. Overall, these findings suggest that Japanese samples cooperate more frequently in repeated interactions than British samples and that this may be due to the assurance-based trust elicited by reciprocal relationships that has been identified as a typical feature of Japanese culture. In situations with incomplete information, expectations about the stake size may guide decision making, with lower expectations resulting in higher cooperation levels.

The persuasive power of knowledge: Testing the confidence heuristic.

According to the confidence heuristic, people are confident when they know they are right, and their confidence makes them persuasive. Previous experiments have investigated the confidence–persuasiveness aspect of the heuristic but not the integrated knowledge–confidence–persuasiveness hypothesis. We report 3 experiments to test the heuristic using incentivized interactive decisions with financial outcomes in which pairs of participants with common interests attempted to identify target stimuli after conferring, only 1 pair member having strong information about the target. Experiment 1, through the use of a facial identification task, confirmed the confidence heuristic. Experiment 2, through the use of geometric shapes as stimuli, elicited a much larger confidence heuristic effect. Experiment 3 found similar confidence heuristic effects through both face-to-face and computer-mediated communication channels, suggesting that verbal rather than nonverbal communication drives the heuristic. Suggesting an answer first was typical of pair members with strong evidence and might therefore be a dominant cue that persuades. Our results establish the confidence heuristic with dissimilar classes of stimuli and through different communication channels.

Persistent Cooperation and Gender Differences in Repeated Prisoner’s Dilemma Games: Some Things Never Change

In the finite-horizon repeated Prisoners Dilemma, a compelling backward induction argument shows that rational players will defect in every round, following the uniquely optimal Nash equilibrium path. It is frequently asserted that cooperation gradually declines when a Prisoners Dilemma is repeated multiple times by the same players, but the evidence for this is unconvincing, and a classic experiment by Rapoport and Chammah in the 1960s reported that cooperation eventually recovers if the game is repeated hundreds of times. They also reported that men paired with men cooperate almost twice as frequently as women paired with women. Our conceptual replication with Prisoners Dilemmas repeated over 300 rounds with no breaks, using more advanced, computerized methodology, revealed no decline in cooperation, apart from endgame effects in the last few rounds, and replicated the substantial gender difference, confirming, in the UK, a puzzling finding first reported in the US in the 1960s.