Asymmetric Information in Simple Bargaining Games: An Experimental Study

Bilateral bargaining situations are often characterized by informational asymmetries concerning the size of what is at stake: in some cases, the proposer is better informed, in others, it is the responder. We analyze the effects of both types of asymmetric information on proposer behavior in two different situations which allow for a variation of responder veto power: the ultimatum and the dictator game. We find that the extent to which proposers demand less in the ultimatum as compared to the dictator game is (marginally) smaller when the proposer is in the superior information position. Further we find informed proposers to exploit their informational advantage by offering an amount that does not reveal the true size of the pie, with proposers in the ultimatum game exhibiting this behavioral pattern to a larger extent than those in the dictator game. Uninformed proposers risk imposed rejection when they ask for more than potentially is at stake, and ask for a risk premium in dictator games. We concentrate on proposers, but also explore responder behavior: We find uninformed responders to enable proposers’ hiding behavior, and we find proposer intentionality not to play an important role for informed responders when they decide whether to accept or reject an offer by an (uninformed) proposer.     

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.     

Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis

This paper reports the findings of a meta-analysis of 37 papers with 75 results from ultimatum game experiments. We find that on average the proposer offers 40% of the pie to the responder. This share is smaller for larger pie sizes and larger when a strategy method is used or when subjects are inexperienced. On average 16% of the offers is rejected. The rejection rate is lower for larger pie sizes and for larger shares offered. Responders are less willing to accept an offer when the strategy method is employed. As the results come from different countries, meta-analysis provides an alternative way to investigate whether bargaining behavior in ultimatum games differs across countries. We find differences in behavior of responders (and not of proposers) across geographical regions. With one exception, these differences cannot be attributed to various cultural traits on which for instance the cultural classifications of Hofstede (1991) and Inglehart (2000) are based.     

Heterogeneous guilt sensitivities and incentive effects

Psychological games of guilt aversion assume that preferences depend on (beliefs about) beliefs and on the guilt sensitivity of the decision-maker. We present an experiment designed to measure guilt sensitivities at the individual level for various stake sizes. We use the data to estimate a structural choice model that allows for heterogeneity, and permits that guilt sensitivities depend on stake size. We find substantial heterogeneity of guilt sensitivities in our population, with 60% of decision makers displaying stake-dependent guilt sensitivity. For these decision makers, we find that average guilt sensitivities are significantly different from zero for all stakes considered, while significantly decreasing with the level of stakes.     

Behavioral spillovers in coordination games

Motivated by problems of coordination failure observed in weak-link games, we experimentally investigate behavioral spillovers for minimum- and median-effort coordination games. Subjects play these coordination games simultaneously and sequentially. The results show that successful coordination on the Pareto optimal equilibrium in the median game influences behavior in the minimum game when the games are played sequentially. Moreover, this positive, Pareto-improving spillover is present even when group composition changes across games, although the effect is not as strong. We also find that the precedent for uncooperative behavior in the minimum game does not influence play in the median game. These findings suggest guidelines for increasing cooperative behavior within organizations.     

Gender differences in lying

Aversion to lying has been consistently observed in sender-receiver games. Women have demonstrated greater aversion to lying for a small monetary benefit in these games than men. We test the robustness of this gender difference in a sender-receiver game with larger stakes. We find no difference in lying by gender.     

The dynamics of responder behavior in ultimatum games: a meta-study

Using data aggregated from seven papers that study repeated play in standard ultimatum games with either stranger or absolute stranger matching, we show that the behavior of responders changes with experience. High offers are more likely to be accepted with experience and low offers are more likely to be rejected. At the individual level, there is a negative relationship between the likelihood that a given offer is accepted and the size of the preceding offer. We compare the results with predictions generated by static models of distributional preferences, implicitly dynamic models of preferences with reciprocity, and explicitly dynamic models of adaptive learning. The data is most consistent with models of preferences with reciprocity.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.     

The Political Economy of Clientelism*

In this paper, we argue that the political‐commitment problem provides an explanation for why much income redistribution takes an inefficient form, particularly employment in the public sector. A job is a credible way of redistributing when it provides rents (such as in situations with moral hazard), and employment is optimal ex post. Moreover, a job is selective and reversible, and thus ties the continuation utility of a voter to the political success of a particular politician. We show that the need to make offers of employment incentive‐compatible leads to inefficiencies in the supply of public goods. We also show that such inefficient redistribution becomes relatively attractive in situations with high inequality and low productivity. Inefficiency is increased when the stakes from politics are high, when inequality is high, and when money matters less than ideology in politics.     

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.     

Equilibrium play and adaptive learning in a three-person centipede game

The two-person centipede game is one of the most celebrated paradoxes of backward induction in complete information extensive form games. An experimental investigation of a three-person centipede game shows that the paradoxical results are strongly affected by the size of the stakes. When the number of players in the game is increased from two to three and the game is played for unusually high stakes with group composition being randomly changed from trial to trial, the paradox is considerably weakened as players approach equilibrium play with multiple iterations of the stage game. When the game is played with low stakes, there is no evidence for equilibrium play or learning across iterations of the stage game. An adaptive learning model that assumes updating of the individual probabilities of choice outperforms alternative static and dynamic models in accounting for the major results observed in the high-stake experiment.     

Timing and Virtual Observability in Ultimatum Bargaining and “Weak Link” Coordination Games

Previous studies have shown that simply knowing one player moves first can affect behavior in games, even when the first-mover's moves are known to be unobservable. This observation violates the game-theoretic principle that timing of unobserved moves is irrelevant, but is consistent with virtual observability, a theory of how timing can matter without the ability to observe actions. However, this previous research only shows that timing matters in games where knowledge that one player moved first can help select that player's preferred equilibrium, presenting an alternative explanation to virtual observability. We extend this work by varying timing of unobservable moves in ultimatum bargaining games and “weak link” coordination games. In the latter, the equilibrium selection explanation does not predict any change in behavior due to timing differences. We find that timing without observability affects behavior in both games, but not substantially.     

Testing theories of behavior for extensive-form two-player two-stage games

We examine choices in two-player extensive-form games that give subjects opportunities for individualistic as well as other-regarding behavior, and where each subject makes choices in a variety of games. Following an extensive search over models, where we estimate a single parameter vector for all the games rather than different parameter vectors for each game, we find that (1) the level-n model organizes the data well, (2) other-regarding behaviors in these games appear to consist primarily of egalitarian and utilitarian behaviors, and (3) there is no significant evidence for reciprocal behavior. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Group play in games and the role of consent in network formation

We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find a stark contrast between how groups and individuals play, with payoffs playing a primary role in equilibrium selection when individuals play, but the structure of the voting rule playing the primary role when groups play. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments.     

EXPLORING THE CONSISTENCY OF HIGHER ORDER RISK PREFERENCES

This study measures higher order risk preferences and their consistency. We explore the role of country differences, the variation of stakes, and the framing of lotteries. We observe a robust dichotomous pattern of choice behavior in China, the United States, and Germany. The majority of choices are consistent with mixed risk aversion or mixed risk-loving behavior. We also find this pattern after a 10-fold increase in the stakes. Finally, our results reveal that this pattern is strengthened if the lotteries are displayed in compound instead of reduced form. In a follow-up study, we explore potential explanations for this framing effect.     

Quantal Response Equilibria for Extensive Form Games

This article investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal-choice model and assume other players do so as well. We define an agent quantal response equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal-choice probabilities are given by logit response functions. AQRE makes predictions that contradict the invariance principle in systematic ways. We show that these predictions match up with some experimental findings by Schotter et al. (1994) about the play of games that differ only with respect to inessential transformations of the extensive form. The logit-AQRE also implies a unique selection from the set of sequential equilibria in generic extensive form games. We examine data from signaling game experiments by Banks et al. (1994) and Brandts and Holt (1993). We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these experiments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment and find that the AQRE model can account for behavior that had previously been explained in terms of altruistic behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analogy-based expectation equilibrium

In complex situations, agents use simplified representations to learn how their environment may react. I assume that agents bundle nodes at which other agents must move into analogy classes, and agents only try to learn the average behavior in every class. Specifically, I propose a new solution concept for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations correctly represent the average behavior in every class. The solution concept is shown to differ from existing concepts, and it is applied to a variety of games, in particular the centipede game, and ultimatum/bargaining games. The approach explains in a new way why players may Pass for a large number of periods in the centipede game, and why the responder need not be stuck to his reservation value in ultimatum games. Some possible avenues for endogenizing the analogy grouping are also suggested.     

Preferences, Property Rights, and Anonymity in Bargaining Games

Research on ultimatum and dictator games has found that because of "fairness" first movers in such games offer more than noncooperative game theory predicts. We find that if the right to be the first mover is "earned" by scoring high on a general knowledge quiz, then first movers behave in a more self-regarding manner. We also conducted dictator double blind experiments, in which the experimenter could not identify the decision maker. The results yielded by far our largest observed incidence of self-regarding offers, suggesting that offers are due to strategic and expectation considerations. Journal of Economic Literature Classification Numbers: C78, C91.     

Higher cognitive ability is associated with lower entries in a p-beauty contest

“Beauty contests” are well-studied, dominance-solvable games that generate two interesting results. First, most behavior does not conform to the unique Nash equilibrium. Second, there is considerable unexplained heterogeneity in behavior. In this work, we explore the relationship between beauty contest behavior and cognitive ability. We find that subjects with high cognitive ability exhibit behavior that is closer to the Nash equilibrium.     

Do people care about social context? Framing effects in dictator games

Many previous experiments document that behavior in multi-person settings responds to the name of the game and the labeling of strategies. With a few exceptions, these studies cannot tell whether frames affect preferences or beliefs. In three large experiments, we investigate whether social framing effects are also present in Dictator games. Since only one of the subjects makes a decision, the frame can affect behavior merely through preferences. In all the experiments, we find that behavior is insensitive to social framing. We discuss how to reconcile the absence of social framing effects in Dictator games with the presence of social framing effects in Ultimatum games.