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.     

Bargaining under a deadline: evidence from the reverse ultimatum game

We study a “reverse” ultimatum game, in which proposers have multiple chances to offer responders a division of some fixed pie. The game ends if the responder accepts an offer, or if, following a rejection, the proposer decides not to make a better offer. The unique subgame perfect equilibrium gives the proposer the minimum possible payoff. Nevertheless, the experimental results are not too different from those of the standard ultimatum game, although proposers generally receive slightly less than half of the surplus.We use the reverse ultimatum game to study deadlines experimentally. With a deadline, the subgame perfect equilibrium prediction is that the proposer gets the entire surplus.Deadlines are used strategically to influence the outcome, and agreements are reached near the deadline. Strategic considerations are evident in the differences in observed behavior between the deadline and no deadline conditions, even though agreements are substantially less extreme than predicted by perfect equilibrium.     

An experimental analysis of ultimatum bargaining

There are many experimental studies of bargaining behavior, but suprisingly enough nearly no attempt has been made to investigate the so-called ultimatum bargaining behavior experimentally. The special property of ultimatum bargaining games is that on every stage of the bargaining process only one player has to decide and that before the last stage the set of outcomes is already restricted to only two results. To make the ultimatum aspect obvious we concentrated on situations with two players and two stages. In the ‘easy games’ a given amount c has to be distributed among the two players, whereas in the ‘complicated games’ the players have to allocate a bundle of black and white chips with different values for both players. We performed two main experiments for easy games as well as for complicated games. By a special experiment it was investigated how the demands of subjects as player 1 are related to their acceptance decisions as player 2.     

On the interpretation of bribery in a laboratory corruption game: moral frames and social norms

Past studies on laboratory corruption games have not been able to find consistent evidence that subjects make “immoral” decisions. A possible reason, and also a critique of laboratory corruption games, is that the experiment may fail to trigger the intended immorality frame in the minds of the participants, leading many to question the very raison d’être of laboratory corruption games. To test this idea, we compare behavior in a harassment bribery game with a strategically identical but neutrally framed ultimatum game. The results show that fewer people, both as briber and bribee, engage in corruption in the bribery frame than in the alternative and the average bribe amount is lesser in the former than in the latter. These suggest that moral costs are indeed at work. A third treatment, which relabels the bribery game in neutral language, indicates that the observed treatment effect arises not from the neutral language of the ultimatum game but from a change in the sense of entitlement between the bribery and ultimatum game frames. To provide further support that the bribery game does measure moral costs, we elicit the shared perceptions of appropriateness of the actions or social norm, under the two frames. We show that the social norm governing the bribery game frame and ultimatum game frame are indeed different and that the perceived sense of social appropriateness plays a crucial role in determining the actual behavior in the two frames. Furthermore, merely relabelling the bribery game in neutral language makes no difference to the social appropriateness norm governing it. This indicates that, just as in the case of actual behavior, the observed difference in social appropriateness norm between bribery game and ultimatum game comes from the difference in entitlement too. Finally, we comment on the external validity of behavior in lab corruption games.     

The Impact of Exchange Context on the Activation of Equity in Ultimatum Games

In this paper we report the results of additional exchange ultimatum game experiments conducted at the same time as the exchange ultimatum game experiments reported in Hoffman et al. (Games and Economic Behavior, 7(3), pp. 346–380, 1994). In these additional experiments, we use instructions to change an impersonal exchange situation to a personal exchange situation. To do this, we prompt sellers to consider what choices their buyers will make. Game theory would predict that thinking about the situation would lead sellers to make smaller offers to buyers. In contrast, we find a significant increase in seller offers to buyers. This result suggests that encouraging sellers to thinking about buyer choices focuses their attention on the strategic interaction with humans who think they way they do in personal exchange situations, and who may punish them for unacceptable behavior, and not on the logic of the game theoretic structure of the problem.     

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.     

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.     

Achieving efficiency with manipulative bargainers

Two agents bargain over the allocation of a bundle of divisible commodities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a family that includes the Nash and the Raiffa–Kalai–Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent's features to virtually implement the Nash bargaining solution.     

Fairness, errors and the power of competition

In this paper, we investigate the effects of competition on bargained outcomes. We show that the neglect of either fairness concerns or decision errors will prevent a satisfactory understanding of how competition affects bargaining. We conducted experiments which demonstrate that introducing a small amount of competition to a bilateral ultimatum game – by adding just one competitor – induces large behavioral changes among responders and proposers, causing large changes in accepted offers. Models that assume that all people are self-interested and fully rational do not adequately explain these changes. We show that a model which combines heterogeneous fairness concerns with decision errors correctly predicts the comparative static effects of changes in competition. Moreover, the combined model is remarkably good at predicting the entire distribution of offers in many different competitive situations.     

Unions and the share economy

This paper contrasts share bargaining and wage bargaining in the context of a “monopoly” model of union bargaining. In the example considered here, employment levels are identical under wage and share systems, but total compensation is higher under share bargaining than under wage bargaining, underscoring the importance of the broader ontext within which a share system is introduced.     

Quantal-response equilibrium models of the ultimatum bargaining game

This paper investigates the implications of quantal response equilibrium (QRE) models [McKelvey and Palfrey, 1995, Games Econ. Behav. 10, 6–38; 1998, Exper. Econ. 1, 9–41] in the ultimatum bargaining game. It is shown that, in a normal-form QRE (NQRE), each bargainer's decision depends critically on the anticipated behavior of the other, and there is a NQRE in which the proposer makes any offer between zero and equal split as a strict best response. The application of NQRE to the experimental data [Slonim and Roth, 1998, Econometrica 66, 569–596] suggests that the history dependence observed in the experiment is a result of the strategic interactions between bargainers.     

Testing subgame perfection apart from fairness in ultimatum games

We present an experiment designed to separate the two commonplace explanations for behavior in ultimatum games—subjects’ concern for fairness versus the failure of subgame perfection as an equilibrium refinement. We employ a tournament structure of the bargaining interaction to eliminate the potential for fairness to influence behavior. Comparing the results of the tournament game with two control treatments affords us a clean test of subgame perfection as well as a measure fairness-induced play. We find after 10 iterations of play that about half of all non-subgame-perfect demands are due to fairness, and the rest to imperfect learning. However, as suggested by models of learning, we also confirm that the ultimatum game presents an especially difficult environment for learning subgame perfection. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C91, D64, J52     

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.     

AN EXPERIMENT WITH ULTIMATUM BARGAINING IN A CHANGING ENVIRONMENT*

We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects’ behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with pre‐specified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame‐perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of “mutants” (virtual players) that were present in their environment.     

Fairness in the Mail and Opportunism in the Internet: A Newspaper Experiment on Ultimatum Bargaining

Abstract. On 11 May 2001, readers of the Berliner Zeitung were invited to participate in an ultimatum bargaining experiment played in the strategy vector mode: each participant chooses not only how much (s)he demands of the DM1,000 pie but also which of the nine possible offers of DM100, 200, …, 900 (s)he would accept or reject. In addition, participants were asked to predict the most frequent type of behavior. Three randomly selected proposer–responder pairs were rewarded according to the rules of ultimatum bargaining and three randomly chosen participants of those who predicted the most frequent type of behavior received a prize of DM500. Decisions could be submitted by mail, fax or via the internet. Behavior is described, statistically analyzed and compared to the usual laboratory ultimatum bargaining results.     

人们关注的是分配动机还是分配结果?——最后通牒实验视角下两种公平观的考察

本文通过设计一组最后通牒实验考察了分配动机的公平和分配结果的公平对人的行为决策的影响,并分别从浙江和北京两地获取了相关实验数据。采用角色随机分配的简化最后通牒实验,通过提议者不同可选分配方案向响应者发送的信号,考察对提议者的"动机是否公平"从而响应者是否有相应的不同拒绝率。实验结果表明,响应者对提议者"分配动机的公平"有显著不同的反应,说明基于动机的互惠偏好确实在人们的行为决策中扮演重要角色。同时本文通过一组修正型的最后通牒实验从分配结果公平的角度考察了其影响机制,发现分别在保证博弈实验中38%的被试拒绝行为,以及免惩罚博弈中89%的被试拒绝行为,不能被差异厌恶偏好理论进行解释。本文实验的结果在于说明分配动机的公平比分配结果的公平更会影响人们的决策行为,其暗含的政策含义即分配过程的公平比分配结果的公平更为重要。     

Non-cooperative bargaining and the incomplete informational core

In an exchange economy with incomplete information, the signaling core is defined by the set of state-contingent allocations to which no coalitions object under informational leakage through proposals by informed agents. An objection underlying the signaling core is supported by a sequential equilibrium of an ultimatum bargaining game with an informed proposer. We prove that a stationary sequential equilibrium allocation in a Rubinstein-type sequential bargaining game with a restart rule belongs to the signaling core if the belief of players satisfies a self-selection property.     

A Note on the Ultimatum Paradox, Bounded Rationality, and Uncertainty

The ultimatum game is a sequential-move bargaining game in which a giver offers a taker a share of a monetary pie. The predicted subgame perfect equilibrium in the ultimatum game is for purely rational givers who act in their own narrow self-interest to offer the smallest possible share of a monetary price, and for purely rational takers to accept. Experimental trials suggest, however, that givers make generous offers because they have a taste for fairness. The analysis presented in this paper argues that it is in the best interest of givers of any type to make offers that will not be rejected, and that offers become more generous as a giver’s uncertainty about the taker’s reservation offer increases.     

Inter-gender interaction and communication in ultimatum games

In this article, we focus on bargaining within male–female pairs, the most pervasive partnership in humankind. We analyse data from an ultimatum game played by Greek participants. Parallel to this, we introduce a one-way communication protocol according to which the responders can send short messages to the receivers, after making their decisions. The analysis shows that gender and message effects exist and males are more effective bargainers.     

Barriers to Global Free Trade through Bilateral Agreements

This paper examines the formation of bilateral free trade agreements (FTAs) in the context of a dynamic noncooperative bargaining game with a random proposer. We show that global free trade (a grand coalition) does not necessarily occur unless transfer payments among countries are allowed. When transfer payments are possible, bilateral FTAs always achieve global free trade, but the ex‐ante and ex‐post inequalities of social welfare among countries are larger than those when all countries are independent because of the strategic bargaining behavior.