How to Model Heterogeneity in Costly Punishment: Insights from Responders' Response Times

We investigate what processes may underlie heterogeneity in social preferences. We address this question by examining participants’ decisions and associated response times across 12 mini-ultimatum games. Using a finite mixture model and cross-validating its classification with a response time analysis, we identified four groups of responders: one group takes little to no account of the proposed split or the foregone allocation and swiftly accepts any positive offer; two groups process primarily the objective properties of the allocations (fairness and kindness) and need more time the more properties need to be examined; and a fourth group, which takes more time than the others, appears to take into account what they would have proposed had they been put in the role of the proposer. We discuss implications of this joint decision–response time analysis. Copyright © 2013 John Wiley & Sons, Ltd. key words ultimatum game; response time; finite mixture model; heterogeneity; altruistic punishment; response time; heuristics Our collective folklore is populated with characters, such as Zorro, Robin Hood, and the Lone Ranger, who fight to right what they perceive of as injustice and in the process punish norm violators. Dirty Harry, the screen cop made famous by Clint Eastwood, even tells the norm violators “Go ahead, make my day,” thus informing them that he will derive satisfaction from punishing them. Clearly, these characters are figments of our imagination, although some may have historical origins. The willingness to enforce norms even if doing so exacts costs to one, however, is not a prerogative of fictional characters but can also be observed in ordinary people. Take, for example, the legion of whistleblowers, such as Daniel Ellsberg, risking their career and retaliation to expose the misconduct on the part of an agency, organization, or a company. Not everybody, however, finds a Robin Hood in himself or herself or finds satisfaction in punishing norm violators. Do economists and psychologists therefore have to assume fundamentally different character or personality traits to explain people’s varying predilections to punish norm violators? Calling upon such distinct traits is indeed the predominant approach in moral philosophy (see Doris, 2002). Alternatively, however, these differences across people could be differences in degree, not kind. The same issue also arises concerning the cognitive processes underlying our choices, which are social in the sense that they also affect other people apart from the decision maker. When making these choices, do all people process the same chunks of information and motives similarly, except that they may weight them differently? Or, do some people recruit processes that are different in kind? We will be concerned with heterogeneity in social choices. People are able to display an amazing range of behaviors towards others. In particular, there is a rich body of empirical evidence showing that humans care about others. They are generous, and they reward the kind actions of others and punish unkind behavior. Their responses, however, can also betray envy and sometimes even spite (e.g., Berg, Dickhaut, & McCabe, 1995; Falk, Fehr, & Fischbacher, 2005; Fehr & Gächter, 2000; Güth, Schmittberger, & Schwarze, 1982). Observations of diverse other-regarding preferences challenge a frequent assumption in economic models, namely, that humans are assumed to be rational decision makers and to harbor purely self-regarding preferences (see Camerer & Fehr, 2006). Several theories have been proposed to accommodate the panoply of other-regarding preferences. All retain the utility framework and account for other-regarding behaviors by either discarding or modifying the assumption of purely self-regarding preferences. Social preference theories modify it by stipulating that, in addition to the material payoff, people’s choices may be guided by the outcomes and behaviors of others. Those other-regarding preferences (henceforth, social motives) are incorporated as additional terms into the utility function. The most prominent among these theories are those by Bolton and Ockenfels (2000), Charness and Rabin (2002), Dufwenberg and Kirchsteiger (2004), Falk and Fischbacher (2006), Fehr and Schmidt (1999), Kirchsteiger (1994), Levine (1998), and Rabin (1993). Common to all is the acknowledgement that humans are heterogeneous in the extent to which they are guided by selfish and social motives. The theories, however, differ in the motives (represented by parameters) that they postulate and in how they combine them. For example, the theories by Bolton and Ockenfels (2000) and Fehr and Schmidt (1999) assume that people value equality and dislike inequity, whereas the theories by Charness and Rabin (2002), Dufwenberg and Kirchsteiger (2004), Falk and Fischbacher (2006), Levine *Correspondence to: Ralph Hertwig, Max Planck Institute for Human Development, Lentzeallee 94, 14195Berlin, Germany. E-mail: [email protected] Copyright © 2013 John Wiley & Sons, Ltd. Journal of Behavioral Decision Making, J. Behav. Dec. Making, 26: 462–476 (2013) Published online 24 January 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/bdm.1779 (1998), and Rabin (1993) assume that people like to reciprocate and hence reward kind and punish unkind behavior. Each theory aspires to describe all humans, capturing heterogeneity by parameterization of the assumed motives. In practice, each theory succeeds in explaining some data but fails in explaining all (see, e.g., Brandts & Sola, 2001; Engelmann & Strobel, 2004; Falk, Fehr, & Fischbacher, 2003, 2008; Falk et al., 2005). In this article, we take a different approach to shed light onto the phenomenon of heterogeneity. Specifically, we take advantage of response times (RTs) in the mini-ultimatum game, a variant of the classic and frequently studied ultimatum game (Güth et al., 1982). Next, we briefly introduce these games and then turn to the standard approach of modeling heterogeneity in social games. Note that a companion piece to the present article is that of Hertwig, Fischbacher, and Bruhin (2013). Their theoretical and empirical analyses focus on models of sequential decision trees. Here, we extend this work by reporting more detailed tests and analyses of people’s behavior and RTs. Furthermore, the present focus is on establishing evidence for heterogeneity between people’s decisions in the mini-ultimatum game and how it can be mapped onto underlying psychological processes. THE ULTIMATUM GAME AND THE MINI-ULTIMATUM GAME The ultimatum game involves two parties who play a single round in which one person, the proposer, suggests how to split a fixed monetary pie, typically provided by the experimenter. This proposed split represents a take-it-or-leave-it offer (an ultimatum) that the other person, the responder, chooses to accept or reject. The interaction between the players is anonymous. If the responder chooses to accept the offer, the division will be implemented. Should the responder decide to reject the proposed division, both players will go away empty-handed. In theory, a purely self-interested responder will accept any proposed positive payoff, no matter how small. Anticipating this choice, a self-interested proposer will offer nothing more than the smallest amount possible. The equilibrium offer (i.e., the division for which no player has anything to gain by doing something differently) thus allocates the smallest positive payoff to the responder and the lion’s share to the proposer. This, however, is not what is typically observed in the laboratories. More than 30 years of research on the ultimatum game has consistently found that responders tend to reject low offers and thus behave at odds with the assumption that they simply maximize their self-interest (see Camerer, 2003; Güth & Tietz, 1990). In our investigation, we employed a variant of this classic social game. The mini-ultimatum game is a sequential twoplayer game. The first mover can choose between two fixed allocations. Then, the second mover can accept or reject this choice. Acceptance means that the allocation will be implemented, whereas rejection means that both players will receive zero. We presented our participants with 12 different mini-ultimatum games and classified them according to their rejection behavior. Subsequently, we used this classification in the analysis of participants’ RTs. HOW TO MODEL HETEROGENEITY? Most theories of social preferences capture only one social motive, be it, for example, inequity aversion (Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999) or reciprocity (Levine, 1998; Rabin, 1993). Moreover, all the models fail to explain the behavior of all participants (e.g., Engelmann & Strobel, 2004). Within parameterized social preference theories, there are at least two ways to respond to this state of affairs. Accepting that the existing theories explain only a subset of respondents, one could model heterogeneity using distinct models for different people. Alternatively, one may aim for a unifying theory that encompasses multiple social motives and that explains heterogeneity by assuming that people differ in the strength and combinations of thesemotives, as has been done, for example, by Charness and Rabin (2002), Cox, Friedman, and Gjerstad (2007), Cox, Friedman, and Sadiraj (2008), or Falk and Fischbacher (2006). The interpretation of degenerated parameter values illustrates how these two approaches differ. Degenerated values (mostly zero values), for instance, for parameters capturing social motives could be interpreted to mean that the person, in reality, operates on the basis of a selfish preference function. Consequently, the person’s choices can be accommodated in terms of a simpler model that altogether omits parameters capturing social motives. The same seemingly selfish behavior, however, could also be consistent with very low values on these social parameter(s). Consequently, such parameters would not be zero but only close to zero; hence, such a person may indeed behave unselfishly in some other situations. The first interpretation of degenerated parameter values implies that heterogeneity is categorical in nature; the second assumes its nature to be gradual. Which is more appropriate? To investigate the nature of heterogeneity in social choice, we use behavioral data and, in addition, a process measure, namely, RT. Our starting premise is as follows: A theory that aims to accommodate all heterogeneity and assumes the same set of parameters (although not parameter values) and the same process (e.g., calculations) for all respondents implies, ceteris paribus, relatively homogeneous response time patterns. Differences only arise to the extent that people differ in terms of processing speed but not in terms of different decision processes. If, however, observed RTs prove to be systematically different across people and games, then such heterogeneity suggests that across people, different processes are at work. The issue of how to model heterogeneity is of importance far beyond research on social games. Take, for illustration, the modeling of individuals’ risky choice between monetary gambles. Expected utility theory assumes heterogeneity to be a matter of degree, not kind, and recruits families of utility functions (such as constant absolute or relative risk aversion) to describe it. Similarly, cumulative prospect theory (Tversky & Kahneman, 1992) captures heterogeneity in terms of Heterogeneity in Costly Punishment 463 U. Fischbacher et al. Copyright © 2013 John Wiley & Sons, Ltd. J. Behav. Dec. Making, 26, 462–476 (2013)