Advice and behavior in intergenerational ultimatum games: An experimental approach

In the real world, when people play a game, they often receive advice from those that have played it before them. Such advice can facilitate the creation of a convention of behavior. This paper studies the impact of advice on the behavior subjects who engage in a non-overlapping generational Ultimatum game where after a subject plays he is replaced by another subject to whom he can offer advice.Our results document the fact that allowing advice fosters the creation of a convention of behavior in Ultimatum games. In addition, by reading the advice offered we conclude that arguments of fairness are rarely used to justify the offers of Senders but are relied upon to justify rejections by Receivers.     

Cognitive ability and human behavior in experimental ultimatum games

Recent researches have shed light on the effect of cognitive ability on economic decision-making. By measuring cognitive ability applying Raven's progressive matrix test, we obtain two significant results that this effect affects decision-making in two types of experimental ultimatum games. First, the higher the cognitive ability, the larger the amount a sender offers when the offer is smaller than or equal to the half split. Second, the higher the responders’ cognitive ability, the smaller the offer they accept, when they accept it or not with the strategy method. This study not only finds new factors that affect decision-making in experimental ultimatum games, but also provides more evidences that cognitive ability influences economic decision-making.     

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.     

Positive- versus zero-sum majoritarian ultimatum games: An experimental study

Politics can involve a movement from a position off the Pareto frontier to a point on it (a positive-sum game as exemplified in the classic [Buchanan, J.M., Tullock, G., 1962. The Calculus of Consent. University of Michigan Press, Ann Arbor] work), or a movement along the Pareto frontier (a zero-sum game as exemplified in the classic [Riker, W., 1962. The theory of political coalitions. Yale University Press, New Haven] work). In this paper we shed light on their differentiation experimentally by making a comparison between a positive-sum and a zero-sum majoritarian ultimatum game. Our main findings include (i) the fraction of subjects who adopted minimum winning rather than oversized coalitions increases significantly as the game form varies from positive-sum to zero-sum, (ii) oversized coalitions are attributable to non-strategic considerations, and (iii) subjects who choose to adopt the minimum winning coalition have a tendency to seek cheaper responders as their partners in the zero-sum game, but there is no evidence of such a tendency in the positive-sum game. Overall, the weight of the evidence revealed by our experimental data indicates that relative scarcity (embodied in the zero-sum game) promotes behavior more in line with the predictions of economics.     

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     

Let me sleep on it: Delay reduces rejection rates in ultimatum games

Delaying acceptance decisions in the Ultimatum Game drastically increases acceptance of low offers. While in treatments without delay less than 20% of low offers are accepted, 60-80% are accepted as we delay the acceptance decision by around 10 min.     

What's in a name? Anonymity and social distance in dictator and ultimatum games

The standard procedure in experimental economics maintains anonymity among laboratory participants, yet many field interactions are conducted with neither complete anonymity nor complete familiarity. When we are involved in interactive situations in the field, we usually have some clues concerning the characteristics of others; however, in some environments (such as e-commerce) these clues may not be very substantial. How will people respond to varying degrees of anonymity and social distance? We consider the effect of one form of social distance on behavior by comparing the standard procedure of playing dictator and ultimatum games with the same games played by participants who knew the family name of their counterparts. When these names were revealed, dictators allocated a significantly larger portion of the pie. However, this information had no significant effect on the offers in the ultimatum game, as it appears that strategic considerations crowd out impulses toward generosity or charity.     

Coherent behavior in noncooperative games

A new concept of mutually expected rationality in noncooperative games is proposed: joint coherence. This is an extension of the “no arbitrage opportunities” axiom that underlies subjective probability theory and a variety of economic models. It sheds light on the controversy over the strategies that can reasonably be recommended to or expected to arise among Bayesian rational players. Joint coherence is shown to support Aumann's position in favor of objective correlated equilibrium, although the common prior assumption is weakened and viewed as a theorem rather than an axiom. An elementary proof of the existence of correlated equilibria is given, and relationships with other solution concepts (Nash equilibrium, independent and correlated rationalizability) are also discussed.     

Stochastic better-reply dynamics in finite games

In this paper, we analyze a model where individuals from finite populations are repeatedly drawn to play a finite game and in every period choose a weakly better reply to a sample distribution from a finite history of past play. For all finite games and sufficiently incomplete information, we prove convergence to minimal sets closed under better replies. This result complements previous findings in a deterministic continuous-time framework and implies convergence to strict Nash equilibria in many well-known classes of games.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market 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.     

Transient and asymptotic dynamics of reinforcement learning in games

Reinforcement learners tend to repeat actions that led to satisfactory outcomes in the past, and avoid choices that resulted in unsatisfactory experiences. This behavior is one of the most widespread adaptation mechanisms in nature. In this paper we fully characterize the dynamics of one of the best known stochastic models of reinforcement learning [Bush, R., Mosteller, F., 1955. Stochastic Models of Learning. Wiley & Sons, New York] for 2-player 2-strategy games. We also provide some extensions for more general games and for a wider class of learning algorithms. Specifically, it is shown that the transient dynamics of Bush and Mosteller's model can be substantially different from its asymptotic behavior. It is also demonstrated that in general—and in sharp contrast to other reinforcement learning models in the literature—the asymptotic dynamics of Bush and Mosteller's model cannot be approximated using the continuous time limit version of its expected motion.     

Transient and asymptotic dynamics of reinforcement learning in games

Reinforcement learners tend to repeat actions that led to satisfactory outcomes in the past, and avoid choices that resulted in unsatisfactory experiences. This behavior is one of the most widespread adaptation mechanisms in nature. In this paper we fully characterize the dynamics of one of the best known stochastic models of reinforcement learning [Bush, R., Mosteller, F., 1955. Stochastic Models of Learning. Wiley & Sons, New York] for 2-player 2-strategy games. We also provide some extensions for more general games and for a wider class of learning algorithms. Specifically, it is shown that the transient dynamics of Bush and Mosteller's model can be substantially different from its asymptotic behavior. It is also demonstrated that in general—and in sharp contrast to other reinforcement learning models in the literature—the asymptotic dynamics of Bush and Mosteller's model cannot be approximated using the continuous time limit version of its expected motion.     

Individual characteristics and behavior in repeated games: an experimental study

Using a laboratory experiment, we investigate whether a variety of behaviors in repeated games are related to an array of individual characteristics that are popular in economics: risk attitude, time preference, trust, trustworthiness, altruism, strategic skills in one-shot matrix games, compliance with first-order stochastic dominance, ability to plan ahead, and gender. We do find some systematic relationships. A subject’s compliance with first-order stochastic dominance as well as, possibly, patience, gender, and altruism have some systematic effects on her behavior in repeated games. At the level of a pair of subjects who are playing a repeated game, each subject’s gender as well as, possibly, patience and ability to choose an available dominant strategy in a one-shot matrix game systematically affect the frequency of the cooperate–cooperate outcome. However, overall, the number of systematic relationships is surprisingly small.     

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.     

Global dynamics in repeated games with additively separable payoffs

This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. Our results are used to show that in a prisoners' dilemma game with mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally.     

Information acquisition in the ultimatum game: An experimental study

We experimentally investigate if free information disadvantages a player relative to when information is unavailable. We study an Ultimatum game where the Proposer, before making an offer, can obtain free information about the Responder's minimum acceptable offer. Theoretically, the Proposer should obtain the information and play a best reply to the Responder's minimum acceptable offer. Thus the Responder should get the largest share of the surplus. We find that an increasing number of Proposers become informed over time. Moreover, the proportion of Proposers who use the information to maximize money earnings increases over time. The majority of information-acquiring Proposers, however, refuse to offer more than one-half and play a best reply only to Responders who accept offers of one-half or less. This, together with a substantial proportion of Proposers who choose to remain uninformed, means that the availability of free information backfires for Proposers only by a little. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, D63, D80     

The dynamics of some duopoly games involving the Market Share and Nichol strategies

The paper analyses the dynamics of some duopoly output games involving the Cournot, Market-Share and Nichol strategies. The model assumes linear price and cost functions and supposes that outputs are adjusted instantaneously at discrete time intervals. For all games considered, equilibrium is either reached after a finite number of moves or a stable approach to equilibrium occurs as t → ∞. In fact, apart from a few uninteresting cases, arising from the oversimplified form of the Market-Share strategy, all equilibrium points lie on specified parts of the firms' Cournot loci.     

Conditional behavior and learning in similar stag hunt games

This paper reports an experiment using Stag Hunt games with different payoff ranges. Specifically, in one treatment for half of the games the payoff dominant and the risk dominant equilibrium coincide and for the other half of the games they conflict; in the second treatment they always conflict. The experiment provides evidence that the payoff range experienced by the participant influences the likelihood of efficient conventions emerging. In particular, experiencing games where payoff dominance and risk dominance coincide appears to make payoff dominance more attractive in games in which they conflict. In the experiment, we also observe conditional behavior emerging with experience. We develop a model of conditional expectations to explain these stylized facts that depends crucially on the assumption that after a brief learning period participants categorize their experience using the same relative bandwidth in both treatments even though the range of experience is twice as large in treatment 1 as it is in treatment 2. The assumption cannot be rejected by the data. The analysis provides a formal example in which increasing experienced diversity by changing the way similar experiences are categorized increases the likelihood of efficient conventions emerging in communities playing similar Stag Hunt games.