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Concept: Ultimatum game


The strong reciprocity model of the evolution of human cooperation has gained some acceptance, partly on the basis of support from experimental findings. The observation that unfair offers in the ultimatum game are frequently rejected constitutes an important piece of the experimental evidence for strong reciprocity. In the present study, we have challenged the idea that the rejection response in the ultimatum game provides evidence of the assumption held by strong reciprocity theorists that negative reciprocity observed in the ultimatum game is inseparably related to positive reciprocity as the two sides of a preference for fairness. The prediction of an inseparable relationship between positive and negative reciprocity was rejected on the basis of the results of a series of experiments that we conducted using the ultimatum game, the dictator game, the trust game, and the prisoner’s dilemma game. We did not find any correlation between the participants' tendencies to reject unfair offers in the ultimatum game and their tendencies to exhibit various prosocial behaviors in the other games, including their inclinations to positively reciprocate in the trust game. The participants' responses to postexperimental questions add support to the view that the rejection of unfair offers in the ultimatum game is a tacit strategy for avoiding the imposition of an inferior status.

Concepts: Game theory, Hypothesis, The Evolution of Cooperation, Prisoner's dilemma, Dictator game, Ultimatum game, Experimental economics, Reciprocity


Egalitarian motives form a powerful force in promoting prosocial behavior and enabling large-scale cooperation in the human species [1]. At the neural level, there is substantial, albeit correlational, evidence suggesting a link between dopamine and such behavior [2, 3]. However, important questions remain about the specific role of dopamine in setting or modulating behavioral sensitivity to prosocial concerns. Here, using a combination of pharmacological tools and economic games, we provide critical evidence for a causal involvement of dopamine in human egalitarian tendencies. Specifically, using the brain penetrant catechol-O-methyl transferase (COMT) inhibitor tolcapone [4, 5], we investigated the causal relationship between dopaminergic mechanisms and two prosocial concerns at the core of a number of widely used economic games: (1) the extent to which individuals directly value the material payoffs of others, i.e., generosity, and (2) the extent to which they are averse to differences between their own payoffs and those of others, i.e., inequity. We found that dopaminergic augmentation via COMT inhibition increased egalitarian tendencies in participants who played an extended version of the dictator game [6]. Strikingly, computational modeling of choice behavior [7] revealed that tolcapone exerted selective effects on inequity aversion, and not on other computational components such as the extent to which individuals directly value the material payoffs of others. Together, these data shed light on the causal relationship between neurochemical systems and human prosocial behavior and have potential implications for our understanding of the complex array of social impairments accompanying neuropsychiatric disorders involving dopaminergic dysregulation.

Concepts: Psychology, Human, Dopamine, Ultimatum game, Experimental economics, Catechol-O-methyl transferase, Egalitarianism, Inequity aversion


How does one deal with unfair behaviors? This subject has long been investigated by various disciplines including philosophy, psychology, economics, and biology. However, our reactions to unfairness differ from one individual to another. Experimental economics studies using the ultimatum game (UG), in which players must decide whether to accept or reject fair or unfair offers, have also shown that there are substantial individual differences in reaction to unfairness. However, little is known about psychological as well as neurobiological mechanisms of this observation. We combined a molecular imaging technique, an economics game, and a personality inventory to elucidate the neurobiological mechanism of heterogeneous reactions to unfairness. Contrary to the common belief that aggressive personalities (impulsivity or hostility) are related to the high rejection rate of unfair offers in UG, we found that individuals with apparently peaceful personalities (straightforwardness and trust) rejected more often and were engaged in personally costly forms of retaliation. Furthermore, individuals with a low level of serotonin transporters in the dorsal raphe nucleus (DRN) are honest and trustful, and thus cannot tolerate unfairness, being candid in expressing their frustrations. In other words, higher central serotonin transmission might allow us to behave adroitly and opportunistically, being good at playing games while pursuing self-interest. We provide unique neurobiological evidence to account for individual differences of reaction to unfairness.

Concepts: Game theory, Psychology, Person, Serotonin, Social rejection, Individualism, Ultimatum game, Raphe nuclei


Laboratory experiments offer an opportunity to isolate human behaviors with a level of precision that is often difficult to obtain using other (survey-based) methods. Yet, experimental tasks are often stripped of any social context, implying that inferences may not directly map to real world contexts. We randomly allocate 632 individuals (grouped randomly into 316 dyads) from small villages in Sierra Leone to four versions of the ultimatum game. In addition to the classic ultimatum game, where both the sender and receiver are anonymous, we reveal the identity of the sender, the receiver or both. This design allows us to explore how fairness behavior is affected by social context in a natural setting where players are drawn from populations that are well-acquainted. We find that average offers increase when the receiver’s identity is revealed, suggesting that anonymous ultimatum games underestimate expected fair offers. This study suggest that researchers wishing to relate laboratory behavior to contexts in which the participants are well-acquainted should consider revealing the identities of the players during game play.

Concepts: Game theory, Experiment, Behavior, Human behavior, Community, Play, Ultimatum game, Sierra Leone


The ultimatum bargaining game (UBG), a widely used method in experimental economics, clearly demonstrates that motives other than pure monetary reward play a role in human economic decision making. In this study, we explore the behaviour and physiological reactions of both responders and proposers in an ultimatum bargaining game using heart rate variability (HRV), a small and nonintrusive technology that allows observation of both sides of an interaction in a normal experimental economics laboratory environment. We find that low offers by a proposer cause signs of mental stress in both the proposer and the responder; that is, both exhibit high ratios of low to high frequency activity in the HRV spectrum.

Concepts: Game theory, Decision making, Economics, Decision theory, Experiment, Hypothesis, Ultimatum game, Money


We exploit the fact that generosity and trustworthiness are highly correlated and the former can thus be a sign of the latter. Subjects decide between a generous and a mean split in a dictator game. Some of them are informed from the start that afterwards they will participate in a trust game and that their choice in the dictator game may matter; others are not informed in advance. In the trust game, before trusters decide whether or not to trust, some trustees can reveal (or conceal) only their true choice in the dictator game, while others can say to trusters, truthfully or otherwise, what they chose. We find that a generous choice made naturally by uninformed trustees and reliably revealed is more effective in persuading trusters to trust than a generous choice that could be strategic or a lie. Moreover, we find that, when they can, mean subjects lie and go on to be untrustworthy.

Concepts: Game theory, Virtue, Social psychology, Dictator game, Ultimatum game


The accumulation of findings that most responders in the ultimatum game reject unfair offers provides evidence that humans are driven by social preferences such as preferences for fairness and prosociality. On the other hand, if and how the proposer’s behavior is affected by social preferences remains unelucidated. We addressed this question for the first time by manipulating the knowledge that the proposer had about the responder’s belief concerning the intentionality of the proposer. In a new game called the “ultimatum game with ambiguous intentions of the proposer (UGAMB),” we made the intentionality of the proposer ambiguous to the recipient. We expected and found that the proposer would make more unfair offers in this new game than in the standard ultimatum game. This expectation can be derived from either the preference-based model or the strategy model of the proposer’s giving decision. The additional finding that more unfair giving in the UGAMB was not mediated by the proposer’s expectation that the recipient would be more willing to accept unfair offers provided support for the preference-based model. Using a psychological measure of cognitive control, the preference-based model received additional support through a conceptual replication of the previous finding that cognitive control of intuitive drive for prosociality in the dictator game, rather than mind reading in the ultimatum game, is responsible for the difference in giving between the two games.

Concepts: Game theory, Psychology, Mind, Thought, Utility, Dictator game, Ultimatum game, Experimental economics


Experiments on bargaining games have repeatedly shown that subjects fail to use backward induction, and that they only rarely make demands in accordance with the subgame perfect equilibrium. In a recent paper, we proposed an alternative model, termed ‘economic harmony’ in which we modified the individual’s utility by defining it as a function of the ratio between the actual and aspired pay-offs. We also abandoned the notion of equilibrium, in favour of a new notion of ‘harmony’, defined as the intersection of strategies, at which all players are equally satisfied. We showed that the proposed model yields excellent predictions of offers in the ultimatum game, and requests in the sequential common pool resource dilemma game. Strikingly, the predicted demand in the ultimatum game is equal to the famous Golden Ratio (approx. 0.62 of the entire pie). The same prediction was recently derived independently by Schuster (Schuster 2017.Sci. Rep.7, 5642). In this paper, we extend the solution to bargaining games with alternating offers. We show that the derived solution predicts the opening demands reported in several experiments, on games with equal and unequal discount factors and game horizons. Our solution also predicts several unexplained findings, including the puzzling ‘disadvantageous counter-offers’, and the insensitivity of opening demands to variations in the players' discount factors, and game horizon. Strikingly, we find that the predicted opening demand in the alternating offers game is also equal to the Golden Ratio.

Concepts: Game theory, Prediction, Ultimatum game, Nash equilibrium, Golden ratio, Subgame perfect equilibrium, Centipede game, Backward induction


Subjects in the loss domain tend to split payoffs equally when bargaining. The ultimatum game offers an ideal mechanism through which social scientists can investigate whether equal splits are the consequence of the proposers' generosity or due to their anticipation that the responders will reject lower offers. This paper experimentally compares ultimatum bargaining that takes place in a loss domain with that under a gains domain. The results reveal that, although responders do not expect more in the loss domain, proposers do make higher offers. As such, proposers reach agreements more often in the loss domain than they do in the gains domain, and responders receive higher payoffs.

Concepts: Game theory, Economics, Science, 2006 albums, The Loss, Ultimatum game, Debut albums, Split


We consider the evolution of fairness and coalition formation in a three-person ultimatum game in which the coalition value depends on its size. Traditional game theory, which assumes selfish and rational players, predicts the largest and efficient coalition with a proposer exploiting most of the total value. In a stochastic evolutionary model (the frequency-dependent Moran process with mutations) where players make errors in estimating the payoffs and strategies of others, evolutionary selection favors the formation of a two-person subcoalition under weak selection and in the low mutation limit if and only if its coalition value exceeds a high proportion (0.7) of that of the largest coalition. Proposers offer 30% to 35% of the subcoalition value to a coalition member, excluding a non-member. Multilateral bargaining is critically different from the bilateral one. Coalition-forming behavior may cause economic inefficiency and social exclusion. Stochastic evolutionary game theory thus provides theoretical support to explain the behavior of human subjects in economic experiments of a three-person ultimatum game.

Concepts: Game theory, Natural selection, Evolution, Economics, Theory, Ultimatum game, Evolutionarily stable strategy, Evolutionary game theory