Interactions between social norms and incentive mechanisms in organizations
IInteractions between social norms and incentivemechanisms in organizations
Ravshanbek Khodzhimatov − − − , StephanLeitner − − − , and Friederike Wall − − − Digital Age Research Center, University of Klagenfurt, 9020 Klagenfurt, Austria [email protected] Department of Management Control and Strategic Management, University ofKlagenfurt, 9020 Klagenfurt, Austria { stephan.leitner, friederike.wall } @aau.at Abstract.
We focus on how individual behavior that complies with so-cial norms interferes with performance-based incentive mechanisms in or-ganizations with multiple distributed decision-making agents. We modelsocial norms to emerge from interactions between agents: agents observeother the agents’ actions and, from these observations, induce what kindof behavior is socially acceptable. By complying with the induced so-cially accepted behavior, agents experience utility. Also, agents get util-ity from a pay-for-performance incentive mechanism. Thus, agents pur-sue two objectives. We place the interaction between social norms andperformance-based incentive mechanisms in the complex environment ofan organization with distributed decision-makers, in which a set of in-terdependent tasks is allocated to multiple agents. The results suggestthat, unless the sets of assigned tasks are highly correlated, complyingwith emergent socially accepted behavior is detrimental to the organi-zation’s performance. However, we find that incentive schemes can helpoffset the performance loss by applying individual-based incentives inenvironments with lower task-complexity and team-based incentives inenvironments with higher task-complexity.
Keywords:
Agent-based modeling and simulation · NK -framework · emergence · socially accepted behavior Norms are defined as behavior that is common within a society or as rules thatare aimed at maintaining specific patterns of behavior which are acceptable to(the majority) of a society [33]. In line with this definition, Sen and Airiau [35]stress that norms facilitate coordination – they refer to Lewis [28] who argues: ”Everyone conforms, everyone expects others to conform, and everyone has goodreason to conform because conforming is in each person’s best interest wheneveryone else plans to conform” , and conclude that norms can be interpreted asexternal correlating signals that promote behavioral coordination. a r X i v : . [ ec on . GN ] F e b R. Khodzhimatov et al.
Despite being a focus of research in many scientific disciplines, a consen-sus about the ontology of norms has not yet been reached [31]. In this paper,we follow the classification introduced by Tuomela et al. [37], who distinguishbetween four types of norms, namely (i) rule norms, (ii) proper social norms,(iii) moral norms, and (iv) prudential norms (see also [33]). They argue thatthe (i) rule norms can be either formal or informal. The former are articulatedand written with formal sanctions and brought into existence by an authority,the latter are articulated but usually not written down, associated with infor-mal sanctions and brought into existence by group members’ mutual implicitor explicit agreement. Morris-Martin et al. [33] add that rule norms are oftenalso referred to as laws. With respect to (ii) social norms , Tuomela et al. [37]distinguish between conventions , which apply to an entire community, society orsocial class, and group-specific norms , which are specific to one or more groups,but not to the entire society. This understanding of social norms is in line withthe definition introduced in Cialdini et al. [9], who add that social norms areusually not accompanied by enforcing laws. Mahmoud et al. [30] stress that so-cial norms can be interpreted as informal rules and standards which entail whatothers expect, e.g., in terms of behavior, and have a non-obligatory character.The latter implies that social norms are self-enforcing and that there are oftensocial processes underlying norms that ensure that non-conforming results in asocial punishment [4,35]. Thus, obeying social norms is often regarded to be ra-tional due to the threat of social sanctions [14]. Finally, Morris-Martin et al. [33]and Tuomela et al. [37] line out that (iii) moral norms are intended to appeal anindividual’s conscience and (iv) prudential norms usually follow the principlesof rationality.In this paper, we adopt the notion of (ii) social norms introduced above.Their presence has been widely recognized in the academic literature. The fieldof multi-agent systems is, for example, concerned with the emergence of socialnorms and their enforcement in agent societies. Recent reviews of research onnorms in multi-agent systems are provided by Morris-Martin et al. [33] andAlechina et al. [2]. Cranefield et al. [11] line out that the way norms are includedin decision making algorithms needs to be explicitly formulated by the designer,while for human agents, norms (and values) are highly entrenched in the decisionmaking process. This is in line with Kohlberg [24], who argues that individualshave an endogenous preference to conform to the behavior of their peers, whichis why social norms play a central role in a multiplicity of contexts in whichhumans interact and make decisions, such as decisions between different coursesof action in organizations or in politics [35].We apply social norms to the context of organizations which consist of col-laborative and distributed decision makers and focus on the interaction betweenemergent social norms (at the level of individuals) and performance-based in-centives, the behavioral implications of this interaction, and its consequences for ocial norms and incentive mechanisms 3 the performance of the overall system. By doing so, we focus on social normswhich emerge from past decisions of fellow agents within an organization [8].The remainder of this paper is organized as follows: Sec. 2 reviews the re-search on social norms, Sec. 3 describes the structure and methodology we use tomodel the simulation of organizational environment with emergent social normsand varying performance-based incentives, Sec. 4 elaborates on results and find-ings, and Sec. 5 concludes this paper.
Considering social norms as key-factors which drive individual behavior is nota new issue in research. Early work on this topic goes back to social approvalof individual behavior [18,36]. A recent survey of interactions between socialnorms and incentives is provided by Festre [15], who argues that social norms aresupplementary motives to self-interest, which is commonly assumed for economicagents. He presents the following two empirical findings to support this assertion:(i) a large proportion of Americans do not apply for welfare programs, evenwhen they are eligible [32], and (ii) in donations to charity, whether the listof contributors is published or not, has an effect on the total amount donated[3,17]. Festre [15] claims that the reason for this behaviour can be traced backto social norms. Festre [15] reviews current studies on social norms in economic theory andconcludes that there might be two explanations for social norms as a driverof individual behavior: (i) the individual desire for conformity and (ii) positiveexternalities. For (i) the individual desire for conformity, she argues that indi-viduals care about their social status (e.g., in terms of popularity or respect)and therefore want to conform to social norms. This explanation is in line withprevious studies [6,38]. With respect to (ii) positive externalities, Festre [15]refers to Coleman [10], who lines out that situations, in which the same out-come satisfies the interests of others, enforce social norms. Consequently, sinceeveryone has incentives to reward others for working towards this outcome, allindividuals have two sources of utility: the reward for the effort one made to-wards the outcome (i.e., the incentives), and the rewards provided by others forhelping to achieve that outcome (in terms of social approval). This argumenta-tion is also in line with Janssen et al. [21] and Huck et al. [19], who argue thatindividual behavior is driven by multiple forces and that interactions may ex-ist among these forces (e.g., in terms of reinforcement or weakening). Festre [15] Note that along with social norms at the individual level, previous research alsoaddresses social norms at the level of organizations: Dowling et al. [12], for exam-ple, conceptualize organizational legitimacy as congruence between the social valuesassociated with an organization’s action and the norms of acceptable behavior inthe social system of the organization. This paper, however, focuses on social norms within an organization. For extensive discussions on the role of social norms in behavioral control, the readeris also referred to [25], [39], and most recently [29] and the literature cited in thesestudies. R. Khodzhimatov et al. adds that previous research has shortcomings in the way it deals with behavioralresponses to norms or changes in norms, and that the interaction between en-dogenous social norms and incentives should be further addressed. The latter isalso in line with K¨ubler [25], who argues that social norms have been consideredas being exogenous (and, thus, not emergent) for (too) long. Some work in thefield of psychology addresses social norms, but puts the focus on the emergencein the sense of learning which type of behavior is socially approved: Paluck etal. [34], for example, are concerned with evolving norms in the context of so-cial networks in schools and Ehrhart et al. [13] address citizenship behavior inorganizational units. Previous research in the field of economics has, amongstothers, addressed how performance-based incentives can change the meaning offollowing a social norm [19,25], and how incentive framing and social norms in-teract with respect to behavioral implications [29]. Moreover, previous researchhas found that, under specific circumstances, monetary incentives can crowd outincentives provided by intrinsic factors, such as social norms [5,21].We implement emergent social norms in the sense of Cialdini et al. [8], whostate that social norms emerge from the shared knowledge about the past be-havior of peers and are determined by the strength of social interactions and thesimilarity of decisions, regardless of the impact of the norms on the outcomes.Thus, we focus on the behavior that is normal in the population, rather thanwhat is declared (morally or otherwise) to be a desired behavior [1,8]. This al-lows us to model the social norms solely as an emergent phenomenon withoutimposing the desirability qualities to particular actions.Fischer and Huddart [16] similarly acknowledge that social norms can emergeendogenously: they argue that there is a complex relationship between individ-ual behavior and social norms within an organization, as they are mutuallydependent. If an agent’s peers are members of the same organization, individualbehavior determines the organization’s social norms, which, in turn, influenceindividual behavior. They acknowledge, however, that individual behavior ofthe members of an organization is affected not only by social norms but also byother means of behavioral control, such as incentive systems. They conclude thatsocial norms (i) emerge endogenously within organizations from the individualbehavior of the organization’s members and their interaction, and (ii) might beendogenously affected by choices related to organizational design elements. Theyexplicitly point out that further investigation of the interaction between socialnorms and incentives is required. This is where we place our research: we studyhow social norms affect the performance in organizations with collaborative anddistributed decision makers and how they interact with performance-based in-centive mechanisms.
This section introduces the model of a stylized organization which is imple-mented as a collective of P agents facing a complex task. The task environmentis based on the N K -framework [23,41,26]. Agents face the dilemma of pursuing ocial norms and incentive mechanisms 5 two objectives simultaneously, namely, to conform to emergent social norms andto maximize their individual (performance-based) utility. We model agents toemploy the approach of goal programming to dissolve this dilemma and observehow interactions between social norms and (performance-based) incentives affectthe organization’s performance for t = { , , . . . , T } periods. The task environ-ment, in which the organization operates, is introduced in Sec. 3.1, while Secs.3.2 and 3.3 characterize the agents and describe how social norms emerge, respec-tively. Section 3.4 describes the agents’ search for better performing solutionsto the decision problem and the approach of goal programming is introduced inSec. 3.5. Finally, Sec. 3.6 provides an overview of the sequence of events duringsimulation runs. We model an organization that faces a complex decision problem that is ex-pressed as the set of M binary choices. The decision problem is segmented intosub-problems which are allocated to P agents, so that each agent faces an N -dimensional sub-problem. We denote the organization’s decision problem by an M -dimensional bitstring x = ( x , x , . . . , x M ), where M = N · P , bits x i repre-sent single tasks, and x i ∈ { , } for i ∈ { , , ..., M } . Without loss of generality,we model tasks to be assigned to agents sequentially, such that agent 1 is re-sponsible for tasks 1-4, agent 2 – for tasks 5-8, and so forth. Formally, agent p ∈ { , , . . . , P } is responsible for the following vector of tasks: x p = ( x p , . . . , x pN ) = (cid:0) x N · ( p − , . . . , x N · p (cid:1) (1)Every task x i for i ∈ { , , . . . , M } is associated with a uniformly distributedperformance contribution φ ( x i ) ∼ U (0 , complex inthat the performance contribution φ ( x i ), might be affected not only by the deci-sion x i , but also by decisions x j , where j (cid:54) = i . We differentiate between two typesof such inter-dependencies: (a) internal inter-dependencies within x p , in whichinterdependence exists between the tasks assigned to agent p , and (b) external inter-dependencies between x p and x q , in which interdependence exists betweenthe tasks assigned to agents p and q , where p (cid:54) = q . We control inter-dependenciesby parameters K, C, S , so that every task interacts with exactly K other tasksinternally and C tasks assigned to S other agents externally [22]. Figure 1 il-lustrates four stylized interaction structures considered in this paper. The figurefeatures M = 16 tasks equally assigned to P = 4 employees for different levelsof complexity.Based on the structure outlined above, we can formally describe the perfor-mance contribution of decision x i as follows: φ ( x i ) = φ ( x i , x i , ..., x i K (cid:124) (cid:123)(cid:122) (cid:125) K internal interdependencies , x i K +1 , ..., x i K + C · S (cid:124) (cid:123)(cid:122) (cid:125) C · S external interdependencies ) , (2)where { i , . . . , i K + C · S } ⊂ { , . . . , M }\ i , and the parameters satisfy 0 ≤ K < N ,0 ≤ C ≤ N , and 0 ≤ S < P . Using Eq. 2, we compute performance landscapes
R. Khodzhimatov et al. for all agents. We indicate time steps by t ∈ { , , . . . , T } . Let x pt and x t be avector of decisions of agent p and a vector of decisions of all agents at time t ,respectively. Then the performance achieved by agent p at time step t is: φ own ( x pt ) = 1 N (cid:88) x i ∈ x pt φ ( x i ) , (3)and the organization’s performance at time step t is: φ org ( x t ) = 1 P P (cid:88) p =1 φ ( x pt ) . (4)In order to capture diversity (or similarity) in the sub-problems allocated toagents, we consider the correlations between the performance landscapes usingthe methodology described in Verel et al. [40]. The performance contributionsof every set of N tasks assigned to agent p are correlated to the performancecontributions of the sets of N tasks assigned to P − ρ ∈ [0 , ρ = 0 and ρ = 1, agents operate onperfectly distinct and perfectly identical performance landscapes, respectively. The agents’ compensation is composed of a fixed and a variable component:without loss of generality, we normalize the former to 0. The latter is based onagent p ’s own performance φ own (see Eq. 3), and the residual performance φ res resulting from decisions of all other agents. Let x − pt be a vector of decisions ofall agents other than p : x − pt = { x qt : q ∈ { , . . . , P }\ p } (5)Then, the residual performance is defined as the mean of own performances ofevery agent other than p : φ res ( x − pt ) = 1 P − · (cid:88) x ∈ x − pt φ own ( x ) , (6)and agent p ’s variable compensation component follows the linear incentivescheme : φ inc ( x pt , x − pt ) = α · φ own ( x pt ) + β · φ res ( x − pt ) , (7)where α + β = 1. In our context linear incentives are as efficient as other contracts inducing non-boundary actions. See [16, p. 1461].ocial norms and incentive mechanisms 7
Internal ( K = 3 , C = S = 0) Low ( K = C = S = 1) Moderate ( K = C = S = 2) High ( K = S = 3 , C = 4) Fig. 1: Stylized interdependence structures with M = 16 tasks equally assignedto P = 4 agents for different levels of complexity. The crossed cells indicate inter-dependencies as follows: let ( i, j ) be coordinates of a crossed cell in row-columnorder, then performance contribution φ ( x i ) depends on decision x j . We implement the emergent social norms using a version of the Social Cogni-tive Optimization algorithm [42]. The algorithm features social sharing libraries ,where agents share and observe the information (i.e., the previous decisions)which they consider in their decision-making later. In our implementation, everyagent has an individual sharing library (as a memory), and the sharing of infor-mation happens unidirectionally in directed social networks. Below we explainthis algorithm in detail.
R. Khodzhimatov et al.
First of all, we differentiate between two types of tasks, namely private and social tasks. Private tasks are unique to agents, i.e., these tasks cover activitieswhich are in the area of expertise of a specific agent; within the stylized organi-zation captured by our model, only one agent will carry out such a task. In anorganization, for example, only the accounting department will be responsiblefor the accounts payable and the monthly payroll. Social tasks, on the contrary,are types of tasks which (in a similar way) concern all agents. In an organization,every department head will have to make decisions related to their managementstyle, irrespective of the department. In our formulation, private tasks are notrelevant to social norms, while social tasks are.Without loss of generality we use the following convention: let N s indicate thenumber of social tasks allocated to each agent. Then the last N s tasks assignedto agent p are social: x p = ( x p , . . . , x pN − N s (cid:124) (cid:123)(cid:122) (cid:125) private tasks , x pN − N s +1 , . . . , x pN (cid:124) (cid:123)(cid:122) (cid:125) social tasks ) (8)At every time step t , agents share the decisions on N s social tasks with D fellow agents in the same organization according to the network structurepredefined by the modeler. Every agent is endowed with a memory L p in whichthe decisions on social tasks, made and shared by other agents, are stored. Dueto cognitive limitations, the agent’s memory is considered to be limited to T L periods. Once the agents’ cognitive capacity is reached, they forget (remove fromtheir memory L p ) the oldest information on their fellow agents’ decisions onsocial tasks, i.e., they just remember what was shared in the last T L periods andforget everything that was shared before. Thus, at every time step t , agent p getsinformation about the decisions made on social tasks x qsoc from D fellow agents q ∈ { p , . . . , p D } ⊆ { , . . . , P }\ p , and stores it for T L time steps in memory L p .Social norms do not form in the organization until time period T L .The extent to which agent p ’s decision at time t , x pt , complies with theemergent social norm is computed as a match rate of the social bits in thememory: φ psoc ( x pt ) = N s · | L pt | (cid:88) x ∈ L pt h ( x psoc , x ) , t > T L , t ≤ T L (9)where | L pt | is the number of entries in agent p ’s memory at time t and h ( x , y )for two equal-length bitstrings x and y of size J is the number of positions atwhich the corresponding bits are equal: h ( x , y ) = J (cid:88) i =1 [ x i == y i ] . (10) We use the bidirectional ring network topology, in which each node is connected toexactly two other nodes with reciprocal unidirectional links, where nodes representagents and the links represent sharing of information.ocial norms and incentive mechanisms 9
If the statement inside the bracket is true, it equals 1, and 0 otherwise [20].
At time t , agent p can observe its own performance in the last period, φ own ( x pt − ),and the decisions of all agents in the organization in the last period after theyare implemented, x t − .In order to come up with new solutions to their decision problems, agentsperform a search in the neighbourhood of x t − as follows: agent p randomlyswitches one decision x i ∈ x p (from 0 to 1, or vice versa), and assumes thatother agents will not switch their decisions . We denote this vector with oneswitched element by ˆ x pt .Next, the agent has to make a decision whether to stick with the status quo, x pt , or to switch to the newly discovered ˆ x pt . The rule for this decision is describedin the next subsection. Agents pursue two objectives simultaneously: they aim at maximizing theirperformance-based incentives formalized in Eq. 7 and, at the same time, want tocomply with the social norms as formalized in Eq. 9. In order to balance thesetwo objectives, agents follow the approach of goal programming [7] as describedbelow.Let g soc and g inc be the goals that agents have for φ soc ( x pt ) and φ inc ( x pt , x − pt ),respectively . Agent p wants to achieve both goals, so that: φ soc ( x pt ) ≥ g soc , and (11a) φ inc ( x pt , x − pt ) ≥ g inc (11b)Let d soc ( x pt ) and d inc ( x pt , x − pt ) be the under-achievements of the set of decisions( x pt , x − pt ) on the goals regarding social norms and performance-based incentivesrespectively (see Eqs. 7 and 9): d soc ( x pt ) = max { g soc − φ soc ( x pt ) , } , (12) d inc ( x pt , x − pt ) = max { g inc − φ inc ( x pt , x − pt ) , } (13)As mentioned before, agent p discovers ˆ x pt – an alternative configuration tothe decision at t , but can only observe what other agents implemented at theprevious time period, x − pt − . Given p ’s information, this agent makes the decision Levinthal [27] describes situations in which agents switch more than one decision ata time as long jumps and states that such scenarios are less likely to occur, as it ishard or risky to change multiple processes simultaneously. Note that agents are homogeneous with respect to goals and that goals are constantover time.0 R. Khodzhimatov et al. to either implement ˆ x pt or to stick with x pt − at t and chooses x pt according tothe following rule: x pt = arg min x ∈{ x pt − , ˆ x pt } w soc · d soc ( x ) + w inc · d inc ( x , x − pt − ) , (14)where w soc and w inc represent the weights for the goal for compliance with thesocial norms ( g soc ) and goal for performance-based incentives ( g inc ) respectively. The simulation model has been implemented in Python 3.7.4. Every simulationround starts with the initialization of the agents’ performance landscapes, theallocation of tasks to P = 4 agents , and the generation of an N -dimensionalbitstring as a starting point of the simulation run (see Sec. 3.1). After initial-ization, agents perform the hill climbing search procedure outlined above (seeSecs. 3.4 and 3.5) and share information regarding their social decisions in theirsocial networks (see Sec. 3.3). The observation period T , the memory span of theemployees T L , and the number of repetitions in a simulation, R , are exogenousparameters, whereby the latter is fixed on the basis of the coefficient of variation.Figure 2 provides an overview of this process and Tab. 1 summarizes the mainparameters used in this paper.Fig. 2: Process overview. Upper actions are performed by the modeler and loweractions are performed by agents. For reliable results, we generate the entire landscapes before the simulation, which iscomputationally feasible for P = 4 given modern RAM sizes. Our sensitivity analyseswith simpler models without entire landscapes, suggest that the results also hold forlarger population sizes.ocial norms and incentive mechanisms 11 Table 1: Main parameters
Parameter Description Value M Total number of tasks 16 P Number of agents 4 N Number of tasks assigned to a single agent 4[
K, C, S ] Internal and external couplings [3 , , , , , , , , ρ Pairwise correlation coefficient betweentasks assigned to different agents 0.3 T L Memory span of agents 20 N S Number of social tasks 2 D Level of social connection (network de-gree) 2 T Observation period 500 R Number of simulation runs per scenario 300[ g inc , g soc ] Goals for performance-based incentives( φ inc ( x pt , x − pt )) and compliance with thesocial norms ( φ soc ( x pt )) [1 . , . w inc , w soc ] Weights for performance-based incentives φ inc ( x pt , x − pt ) and compliance with the so-cial norms φ soc ( x pt ) [1 , . , . . , . α, β ] Shares of own and residual performancesincluded in the performance-based incen-tive scheme [1 , . , . . , . . , . We indicate the solution (at the system’s level) implemented at time step t and simulation run r ∈ { , . . . , R } by x rt , and the associated performance by φ rorg ( x rt ) (see Eq. 4). As the performance landscapes on which agents operate arerandomly generated, for every simulation run, we normalize the performances bythe maximum performances per landscape to ensure comparability. We indicatethen normalized performance achieved by the organization at time step t insimulation run r by Φ [ r, t ] = φ rorg ( x rt )max x ∈ [0 , M { φ rorg ( x ) } (15)We denote the average performance at t by: Φ [ t ] = 1 R R (cid:88) r =1 Φ [ r, t ] , (16)In Sec. 4.2, we report the distance to maximum performance as a perfor-mance measure. Note that this measure captures the cumulative distance be-tween the average performances achieved throughout the observation period Noteam-basedincentives Lowteam-basedincentives Moderateteam-basedincentives Highteam-basedincentivesHighsocialnormsModeratesocialnormsNosocialnorms (a) Internal complexity ( K = 3 , C = S = 0) Noteam-basedincentives Lowteam-basedincentives Moderateteam-basedincentives Highteam-basedincentivesHighsocialnormsModeratesocialnormsNosocialnorms (b) Low complexity ( K = C = S = 1) Noteam-basedincentives Lowteam-basedincentives Moderateteam-basedincentives Highteam-basedincentivesHighsocialnormsModeratesocialnormsNosocialnorms (c) Moderate complexity ( K = C = S = 2) Noteam-basedincentives Lowteam-basedincentives Moderateteam-basedincentives Highteam-basedincentivesHighsocialnormsModeratesocialnormsNosocialnorms (d) High complexity ( K = S = 3 , C = 4) Fig. 3: Contour plots for cumulative distances d ( Φ ) to the maximum attain-able performance for different scenarios. The lower (higher) values mean better(worse) performance for organization and are indicated by lighter (darker) tonesand the maximum performance attainable (which equals 1 by construction),and lower (higher) values of the distance indicate higher (lower) performance: d ( Φ ) = T (cid:88) t =1 (cid:0) − Φ [ t ] (cid:1) (17) The parameters summarized in Tab. 1 result in 4 · · ocial norms and incentive mechanisms 13 and zero weight on social norms), and 4 different settings for the performance-based incentive schemes (zero, low, moderate, and high team-based incentives).The results are presented in Fig. 3. The contours indicate ranges of similardistance values, where darker (lighter) colors indicate larger (smaller) values forthe distance to maximum. In other words, the lighter contours represent higherorganizational performance and are more desirable, while the darker contoursrepresent lower organizational performance and are less desirable. In each plot,the performance-based incentive scheme ( α and β ) and the pairs of weightsfor incentives and social norms ( w inc and w soc ) are presented as the horizontaland the vertical axes, respectively. Please note that performance-based incen-tive schemes that put full weight on the performance achieved by the agentsindividually are included on the left hand side on horizontal axes (i.e., α = 1and β = 0), while moving to the right decreases the weight of individual per-formance and increases the weight of residual performance (until α = 0 .
25 and β = 0 . w inc = 0 . w soc = 0 . w inc = 1 and w soc = 0). The 4 contour plotscorrespond to 4 different levels of complexity presented in Fig. 1.Looking at the ranges of the plots (the minimal and maximal values), weobserve that as the complexity increases, the average performance drops for allsocial norm weights and incentive schemes. This finding is in line with previousresearch [22,27].For scenarios in which agents put full emphasis on performance-based incen-tives and do not care about complying with social norms (i.e., upper parts ofsubplots, where w inc = 1 and w soc = 0), we can observe that the choice of theincentive scheme does not have an effect on performance in the absence of ex-ternal interdependencies (see Fig. 3 (a)). However as soon as there are externalinterdependencies, even if the task’s complexity is relatively low (see Fig. 3 (b)),the team-based incentive schemes result in a better performance. This positiveeffect of team-based incentive mechanisms increases with the external complex-ity of the task environment (see Fig. 3 (b,c,d)). This finding emphasizes theimportance of differentiating between internal and external interdependenciesamong tasks when designing incentive mechanisms. A stronger focus of incen-tives on the residual performance (higher values of β ) appears to offset some ofthe negative effects associated with task complexity only in cases in which thecomplexity is not internal (i.e., when C, S > Please note that task complexity in Fig. 3 (b) is relatively low, since every task iscoupled with K + C · S = 2 other tasks. In Fig. 3 (a), on the contrary, each task iscoupled with K + C · S = 3 other tasks.4 R. Khodzhimatov et al. We also observe that as the agents start putting higher weights on the socialnorms (i.e. moving down the vertical axis), the contours get darker, meaningthat the performance drops. This represents that complying to social norms cancome at a cost for performance, as agents have to consider multiple objectives.However, as the (external) complexity increases (Fig. 3 (b,c,d)), the extent ofthis effect declines, and in situations with high (external) complexity (see Fig. 3(d)) we observe that the contours are almost vertical, meaning that social normsdo not cause a significant decline in the performance. This can be explainedby the coordinating function of social norms, which can be observed when thetask environment is too complex to solve individually without any coordination.Apart from that, our sensitivity analyses show that the decline in performance re-lated to social norms, disappears for cases with higher correlation among agents’performance landscapes even for environments with lower complexity.
In this paper, we proposed a model of an organization which is composed ofautonomous and collaborative decision making agents facing a complex task.Agents pursue two objectives simultaneously, i.e., they aim at maximizing theirperformance-based incentives and, at the same time, want to comply to the socialnorms emerging in their social networks. In our analysis, we focus on the inter-play between performance-based incentives and social norms. Our main resultsare the following: First, if agents focus on performance-based incentives only, thechoice of the type of incentive scheme has marginal effects in task environmentswith low level of complexity. As complexity increases, team-based incentives be-come more beneficial. However, in environments where inter-dependencies (nomatter how high) exist only within tasks allocated to the same agent, the in-centive schemes have zero effect on the performance. Second, if agents focus oncomplying to social norms, this comes at the cost of performance at the levelof the system (except for scenarios when agents’ task environments are highlycorrelated). Third, whether team-based performance can offset negative effectson performance, caused by agents that aim at complying to social norms, issubstantially affected by the level of task complexity. For highly complex tasks,team-based incentives appear to be beneficial, while the opposite is true for taskenvironments with a low level of complexity.Our work is, of course, not without its limitations. First, we treat complianceand non-compliance to social norms equally. In reality, however, non-complianceto social norms might lead to more fatal consequences than “over-compliance”[15]. Future work might want to investigate this issue. Second, we limit thenumber of agents to 4 and consider ring networks only. It might be a promisingavenue for future research to increase the number of agents and test the effect ofother network topologies on the dynamics emerging from social norms. Finally,it might be an interesting extension to model the transformation of social normsinto values by adjusting the task environment dynamically. ocial norms and incentive mechanisms 15
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