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.     

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.     

Blindfolded vs. Informed Ultimatum Bargaining – A Theoretical and Experimental Analysis

This paper analyzes blindfolded vs. informed ultimatum bargaining where proposer and responder are both either uninformed or informed about the size of the pie. Considering the transition from one information setting to another suggests that more information induces lower (higher) price offers and acceptance thresholds when the pie is small (large). While our experimental data confirm this transition effect, risk aversion leads to diverging results in blindfolded ultimatum bargaining where task‐independent strategies such as ‘equal sharing’ or the ‘golden mean’ are implemented more frequently.     

The powerless yet relevant third: a three-player ultimatum/dictator game with earned funds and roles

We report the first experiment to pair a three-player ultimatum/dictator game with a real effort task. The inclusion of the real effort task shifts the standard for division from simple egalitarianism towards relative performance; even in treatments in which roles and funds are exogenous. Additionally, we find proposers overcompensate themselves relative to their effort, and this additional compensation comes at the expense of powerless (third) players. Individual characteristics predict the nature of a proposals. Lastly, we find that responders’ choice to accept is based on their own and the powerless third party’s compensation.     

Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games

Learning models predict that the relative speed at which players in a game adjust their behavior has a critical influence on long term behavior. In an ultimatum game, the prediction is that proposers learn not to make small offers faster than responders learn not to reject them. We experimentally test whether relative speed of learning has the predicted effect, by manipulating the amount of experience accumulated by proposers and responders. The experiment allows the predicted learning by responders to be observed, for the first time.     

Reinforcement and Directional Learning in the Ultimatum Game with Responder Competition

Demands in the Ultimatum Game in its traditional form with one proposer and one responder are compared with demands in an Ultimatum Game with responder competition. In this modified form one proposer faces three responders who can accept or reject the split of the pie. Initial demands in both ultimatum games are quite similar, however in the course of the experiment, demands in the ultimatum game with responder competition are significantly higher than in the traditional case with repeated random matching. Individual round-to-round changes of choices that are consistent with directional learning are the driving forces behind the differences between the two learning curves and cannot be tracked by an adjustment process in response to accumulated reinforcements. The importance of combining reinforcement and directional learning is addressed. Moreover, learning transfer between the two ultimatum games is analyzed.     

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.     

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。     

Choosing Bargaining Partners—An Experimental Study on the Impact of Information About Income,Status and Gender

Ultimatum proposals and dictator donations are studied when proposers can choose the income and sex of the responder. Responder attributes generated strong effects in the selection decisions; subjects preferred to send proposals to low-income responders and female responders were much more popular than males. Hence, signals of income and sex appear to be important in deciding with whom to bargain. We also report from an experiment where both responders and proposers could select co-player based on socioeconomic status and gender. Both female responders and proposers were strongly preferred. A weaker tendency was that high status subjects were favored.JEL Classification: C90, C78, J7, D63     

Ultimatum Bargaining Behavior in Israel, Japan, Slovenia, and the United States: A Social Utility Analysis

We explain the main features of the results of the four-country ultimatum bargaining experiments of Roth et al. (1991), Amer. Econom. Rev.81, 1068–1095) by a social utility model. The specification of social utility of a player has two parts: a linear combination of the monetary payoffs of the proposer and the responder and payoff uncertainty. We find that, on average, responders have negative regard for proposers' earnings in all countries. Proposers have negative regard for responders' monetary earnings in countries where responders have high negative regard for proposers' earnings (USA and Slovenia). In countries where responders have low negative regard for proposers' earnings (Israel and Japan), proposers are expected payoff maximizers. Journal of Economic Literature Classification Numbers: A13, C19, C44, C72, C92, D63, D64.     

The effect of luck framing on distributional preferences

This paper experimentally investigated luck framing. Specifically, we analyzed the difference between being assigned an advantageous role in a distribution game and being assigned the same role while being explicitly told that you were lucky to be in that favorable position. We tested this difference by implementing a dictator game and a no-veto-cost ultimatum game. We observed that: a) dictators transferred larger amounts in the game when they were explicitly told they were lucky to be the dictator compared to dictators who did not receive this message, and b) responders in the no-veto-cost ultimatum game who were explicitly told they were lucky to be in that role were significantly less likely to reject a particular offer compared to responders in the game who did not receive this message. The combination of these results is consistent with the hypothesis that people are more likely to behave in a more prosocial and egalitarian manner when they are reminded that they are lucky to be in a particular position.     

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.     

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.     

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.     

Promises in group decision making

We assess in the laboratory the effect of promises on group decision-making. The gift-exchange game provides the testing ground for our experiment. When the game is played between groups, inter-group cooperation and reciprocity represent a condition for increasing total earnings as a measure of social efficiency. Our findings show that promises have positive effect on aggregate payoffs and that effect is reinforced when a group member is randomly selected as proposer to set forth an effort/transfer level that other group members can approve or reject. Promises and proposers elicit social conformity leading groups to exhibit more desirable social behavior.     

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.     

From ultimatum to Nash bargaining: Theory and experimental evidence

We consider a sequential two-party bargaining game with uncertain information transmission. When the first mover states her demand she does only know the probability with which the second mover will be informed about it. The informed second mover can either accept or reject the offer and payoffs are determined as in the ultimatum game. Otherwise the uninformed second mover states his own demand and payoffs are determined as in the Nash demand game. In the experiment we vary the commonly known probability of information transmission. Our main finding is that first movers’ and uninformed second movers’ demands adjust to this probability as qualitatively predicted, that is, first movers’ (uninformed second movers’) demands are lower (higher) the lower the probability of information transmission. JEL Classification C72 · C78 · C92     

Competition for Power and Altruism

The paper analyzes the trade-off between power and altruism by using an experimental framework which involved a group of experimental agents, undergraduate students of the University of Siena. The results show that the introduction into the experimental structure of a tournament for the power appreciably altered the behaviour of agents. More specifically the degree of altruism, measured by the dictator offers, significantly decreased when the agents were able to trade altruism for power. The results were more clear-cut and robust in the case of the dictator game, but also in the case of the ultimatum game the introduction of the tournament for power altered the behavior of subjects. A significant gender effect emerged.     

On Perceptions of Fairness: The Role of Valuations, Outside Options, and Information in Ultimatum Bargaining Games

This study examines fairness perceptions in ultimatum bargaining games with asymmetric payoffs, outside options, and different information states. Fairness perceptions were dependent on treatment conditions. Specifically, when proposers had higher chip values, dollar offers were lower than when responders had higher chip values. When responders had an outside option, offers were higher and were rejected less often than when proposers had an outside option. However, a given offer was rejected more often when responders had an outside option. Therefore, similar to the first mover advantage, the “advantaged” or “entitled” player received a higher monetary payoff than they would otherwise. When there was complete information about payoff amounts (payoff conversion rates and outside options), rejections occurred more often, and given offer amounts were rejected more often than when there was incomplete information. When there was incomplete information, offers were higher in the initial rounds than in the final rounds. These results suggest that proposers made offers strategically, making offers that would not be rejected, rather than out of a concern for fairness.     

Reciprocity—an indirect evolutionary analysis

This paper investigates agents who face a stylized pecuniary ‘game of life’ comprising the ultimatum game and the dictator game. Utility may but need not be attached to equity and reciprocity, as formalized by Falk and Fischbacher (Games Econom Behav, 54(2): 293–315, 2006) but, critically, this social component of preferences cannot be conditioned on whether an ultimatum or a dictator game is played. Evolutionary fitness of agents is determined solely by material success. Under these conditions, a strong preference for reciprocity, but little interest in equity as such evolves. Possible exogenous constraints that link reciprocity and equity concerns imply long-run levels of both which depend on the relative frequency of ultimatum vs. dictator interaction in agents’ multi-game environment. Financial support from the German Academic Exchange Service (DAAD) is gratefully acknowledged.