Player Types and Self-Impression Management in Dictatorship Games: Two Experiments

Recent experimental research on dictatorship games shows that many dictators share their outcomes with unknown, anonymous others. The data suggests that dictators can be “typed” as rational (taking the maximum), equal (splitting outcomes equally), or “other.” This paper experimentally tests the self-impression management model, which predicts that individuals act to show themselves in a positive light, even when they are the only observer of their own behavior. The model predicts that the “other” type of dictator will avoid being greedy by taking more only as their choices are increasingly restricted. Results from two experiments support the model's predictions. The conclusion advocates differentiating basic psychological motivations in modeling individual behavior. Journal of Economic Literature Classification Numbers: C78, C91, D63.     

Implications of trust, fear, and reciprocity for modeling economic behavior

This paper reports three experiments with triadic or dyadic designs. The experiments include the moonlighting game in which first-mover actions can elicit positively or negatively reciprocal reactions from second movers. First movers can be motivated by trust in positive reciprocity or fear of negative reciprocity, in addition to unconditional other-regarding preferences. Second movers can be motivated by unconditional other-regarding preferences as well as positive or negative reciprocity. The experimental designs include control treatments that discriminate among actions with alternative motivations. Data from our three experiments and a fourth one are used to explore methodological questions, including the effects on behavioral hypothesis tests of within-subjects vs. across-subjects designs, single-blind vs. double-blind payoffs, random vs. dictator first-mover control treatments, and strategy responses vs. sequential play. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, C91, D63, D64     

The Hot Versus Cold Effect in a Simple Bargaining Experiment

In this paper, the strategy method's impact on behavior in sequential bargaining games is investigated. Besides the decision procedure (hot versus cold), we varied the second mover punishment costs (high versus low). Significant impacts of both treatment variables were observed. For example, second movers punished significantly more often in the hot version of the low cost game. Furthermore, first mover behavior was significantly different in the hot and cold versions of both games. In the hot games, first mover behavior suggests an expectation of decreased rewards and/or punishments from second movers. We observed, however, no decrease in reward and an increase in punishment. The hot cold variable only informs first movers that the decision procedure used by second movers has changed. Therefore, first mover behavior must be shaped by their perceived assessment concerning how second movers make decisions. We argue that first mover behavior can be explained by the interaction of two well-known psychological effects: the consensus and positive self-image effects.     

Belief-Based Refinements in Signalling Games

There are many economic problems which, when modelled as games of incomplete information, give rise to many sequential equilibria, severely limiting the usefulness of the model. There has recently been a large literature devoted to "refining" the set of equilibria in order to reduce this multiplicity by restricting the set of admissible disequilibrium beliefs. This paper argues that the logical foundations of some refinements and the equilibria they focus on are problematic and, further, proposes an alternative refinement that avoids the difficulties. We also provide an existence theorem covering a broad class of signalling games often studied in economics. Journal of Economic Literature Classification Numbers: C72, C70, D82.     

The Statistical Mechanics of Best-Response Strategy Revision

This paper compares local and global strategic interaction when players update using the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice suffices to achieve coordination on the risk-dominant strategy in symmetric 2 × 2 coordination games. The "persistant randomness" which is necessary to achieve similar coordination with global interaction is replaced under local interaction by spatial variation in the initial condition. An extension of the risk-dominance idea gives the same convergence result for K × K games with strategic complementarities. Similar results for K × K pure coordination games and potential games are also presented. Journal of Economic Literature Classification Number: C78.     

Identity and in-group/out-group differentiation in work and giving behaviors: Experimental evidence

We investigate the existence and relative strength of favoritism for in-group versus out-group along multiple identity categories (body type, political views, nationality, religion, and more) in four alternative contexts: (1) giving money in a dictator game, (2) sharing an office, (3) commuting, and (4) work. We carried out two studies. The first study entailed hypothetical situations and imaginary people; the second study was similar to the first, but the dictator game component was incentivized (actual money) and involved actual receivers. Our subjects’ behavior towards others is significantly affected by their respective identities. (1) Those that belong to the in-group are treated more favorably than those who belong to the out-group in nearly all identity categories and in all contexts. (2) Family and kinship are the most powerful source of differentiation, followed by political views, religion, sports-team loyalty, and music preferences, with gender being basically insignificant. (3) The hierarchy of identity categories is fairly stable across the four contexts. (4) Subjects give similar amounts and discriminate between in-group and out-group to similar degrees in the hypothetical and incentivized dictator games.     

Expressed preferences and behavior in experimental games

Participants in experimental games typically can only choose actions, without making comments about other participants' future actions. In sequential two-person games, we allow first movers to express a preference between responder choices. We find that responder behavior differs substantially according to whether first movers express a hope for favorable or unfavorable treatment. Responders largely ignore first movers' expressed preferences for favorable responses, however, when the first movers misbehave. As in earlier experiments without preference expression, subjects assign a high positive weight to another person's payoffs when ahead and misbehavior elicits a strong negative response. Logit regressions estimate the weight placed on another (non-misbehaving) person's payoffs to be positive, even when one is behind. There is suggestive evidence that positive reciprocity is enhanced when a preference for favorable treatment is expressed.     

Of mice and men: Within gender variation in strategic behavior

We study behavioral differences across and within genders in a family of ultimatum and dictator games. We find these differences are due not only to altruistic preferences but also beliefs about the strategic behavior of others. The behavior of men in strategic situations is not significantly more aggressive than women on average. But this average masks wide variation in intra-gender behavior. In particular, a sizable minority of males are “mice,” behaving timidly in strategic environments. Our experimental design shows that the standard ultimatum game can mask significant inter- and intra-gender differences in strategic behavior. These behavioral patterns in strategic environments are shown to be correlated with preferences for altruism in non-strategic settings. Such gender differences could well manifest themselves in real-world large-stakes transactions, such as salary negotiations.     

Infinite horizon common interest games with perfect information

We consider infinite horizon common interest games with perfect information. A game is a K-coordination game if each player can decrease other players' payoffs by at most K times his own cost of punishment. The number K represents the degree of commonality of payoffs among the players. The smaller K is, the more interest the players share. A K-coordination game tapers off if the greatest payoff variation conditional on the first t periods of an efficient history converges to 0 at a rate faster than K^−t as t→∞. We show that every subgame perfect equilibrium outcome is efficient in any tapering-off game with perfect information. Applications include asynchronously repeated games, repeated games of extensive form games, asymptotically finite horizon games, and asymptotically pure coordination games.     

Dictator monopolies and essential goods: experimental evidence

Monopolists set prices and if the good is unessential this may place the consumer in an uncomfortable position. But if the good is essential the consumer faces a pay-to-live or -die choice. Dictator and ultimatum games are superficially similar in that one game offers the right of refusal, while the other does not. The dictator monopoly is, however, not a game, and behaviour could be radically different in the market environment versus game environment. We recast the dictator game as a dictator monopoly experiment and find that the fairness characteristic of the game evaporates quickly as rounds progress.     

Quasi-weightings, Trading, and Desirability Relations in Simple Games

We investigate the problem of simultaneously characterizing various classes of simple games in three different ways: (i) the existence of “quasi-weightings” in which smaller numerical values are assigned to losing coalitions than are assigned to winning ones, (ii) the robustness of “winningness” with respect to trades involving groups of players, and (iii) the acyclicity of certain strict “orderings” that intuitively correspond to the idea of one player being more desirable than another.Journal of Economic LiteratureClassification Number: C71.     

Perfect versus Imperfect Observability—An Experimental Test of Bagwell's Result

In a seminal paper Bagwell ((1995). Games Econom. Behav.8, 271–280) claims that the first mover advantage, i.e., the strategic benefit of committing oneself to an action before others can, vanishes completely if this action is only imperfectly observed by second movers. In our paper we report on an experimental test of this prediction. We implement four versions of a game similar to an example given by Bagwell, each time varying the quality of the signal which informs the second mover. For experienced players we do not find empirical support for Bagwell's result. Journal of Economic Literature Classification Numbers: C72, C92.     

Altruism in Anonymous Dictator Games

We conduct double-anonymous dictator experiments to explore the role of altruism in motivating subjects' behavior. We vary the extent to which an anonymous recipient is deserving of aid and investigate its effect on the allocation of a fixed pie by student subjects. This is accomplished by including as treatments: (1) an anonymous student subject and (2) an established charity. We find that a significant increase in donations occurs when we increase the extent to which a donation goes to a recipient generally agreed to be “deserving.” We conclude that subjects are rational in the way they incorporate fairness into their decisions.Journal of Economic LiteratureClassification Numbers: A13, C91, D64.     

Contagion of Self‐Interested Behavior: Evidence from Group Dictator Game Experiments

We examine how group decision‐making affects other‐regarding behavior in experimental dictator games. In particular, we assess whether the effects of iterated games differ for group and individual decision‐making and whether the difference in decision‐making style (individual or group) changes the perception of social identity. We make two findings on group decision‐making. First, group decisions become more selfish when repeating the game after changing group members. Second, a dictator group donates more to a recipient group at the same university than to a recipient group at a different university. These findings are not true for individual decision‐making.     

Self-Fulfilling Mechanisms in Bayesian Games

Amechanismfor a Bayesian gameGis a mapping μ from the set of states of nature to the set of players' actions. μ isself-fulfillingif players are truthful at the communication stage and, given the information revealed by μ, no player can gain in unilaterally deviating from the action prescribed by the mechanism. We investigate the properties of self-fulfilling mechanisms and we show in particular that they correspond to inert solutions of the infinitely repeated game generated byG. We also discuss applications to market games, regulation, and R&D games.Journal of Economic LiteratureClassification Numbers: D82, C72.     

A Note on the Probability of k Pure Nash Equilibria in Matrix Games

A formula is derived for the probability that a "randomly selected" n-person matrix game has exactly k pure strategy equilibria. It is shown that for all n ≥ 2, this probability converges to e⁻¹/k! as the sizes of the strategy sets of at least two players increase without bound. Thus the number of pure strategy equilibria in large random n-person matrix games is approximately Poisson distributed with mean one. The latter is a known result obtained by a new proof in this note. Journal of Economic Literature Classification Number: C72.     

Abreu–Matsushima Mechanisms: Experimental Evidence

Abreu–Matsushima mechanisms can be applied to a broad class of games to induce any desired outcome as the unique rationalizable outcome. We conduct experiments investigating the performance of such mechanisms in two simple coordination games. In these games one pure-strategy equilibrium is “focal”; we assess the efficacy of Abreu–Matsushima mechanisms for implementing the other pure-strategy equilibrium outcome. Abreu–Matsushima mechanisms induce some choices consistent with the desired outcome, but more choices reflect the focal outcome. Moreover, “strengthening” the mechanism has a perverse effect when the desired outcome is a Pareto-dominated risk-dominated equilibrium.Journal of Economic LiteratureClassification Number: C7.     

The α-beauty contest: Choosing numbers, thinking intervals

We present a model for the α-beauty contest that explains common patterns in experimental data of one-shot and iterative games. The approach is based on two basic assumptions. First, players iteratively update their recent guesses. Second, players estimate intervals rather than exact numbers to cope with incomplete knowledge of other players' rationality. Under these assumptions we extend the cognitive hierarchy model of Camerer et al. [Camerer, C., Ho, T., Chong, J., 2003b. A cognitive hierarchy model of one-shot games. Quart. J. Econ. 119, 861–898]. The extended model is estimated on experimental data from a newspaper experiment.     

Taking,giving, and impure altruism in dictator games

We show that, if giving is equivalent to not taking, impure altruism could account for List’s (in Journal of Political Economy 115(3):482–493, 2007) finding that the payoff to recipients in a dictator game decreases when the dictator has the option to take. We examine behavior in dictator games with different taking options but equivalent final payoff possibilities. We find that recipients tend to earn more as the amount the dictator must take to achieve a given final payoff increases, a result consistent with the hypothesis that the cold prickle of taking is stronger than the warm glow of giving. We conclude that not taking is not equivalent to giving and agree with List (in Journal of Political Economy 115(3):482–493, 2007) that the current social preference models fail to rationalize the observed data.     

Learning to Learn, Pattern Recognition, and Nash Equilibrium

The paper studies a large class of bounded-rationality, probabilistic learning models on strategic-form games. The main assumption is that players “recognize” cyclic patterns in the observed history of play. The main result is convergence with probability one to a fixed pattern of pure strategy Nash equilibria, in a large class of “simple games” in which the pure equilibria are nicely spread along the lattice of the game. We also prove that a necessary condition for convergence of behavior to a mixed strategy Nash equilibrium is that the players consider arbitrarily long histories when forming their predictions.Journal of Economic LiteratureClassification Numbers: C72, D83.