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Randomness and Arbitrary Coordination in the Reactive Ultimatum Game  [PDF]
Roberto da Silva,Pablo A. Valverde,Luis C. Lamb
Physics , 2015,
Abstract: Darwin's theory of evolution - as introduced in game theory by Maynard Smith - is not the only important evolutionary aspect in a evolutionary dynamics, since complex interdependencies, competition, and growth should be modeled by, for example, reactive aspects. In the ultimatum game the reciprocity and the fifty-fifty partition seems to be a deviation from rational behavior of the players under the light of the Nash equilibrium concept.Such equilibrium emerges, for example, from the punishment of the responder who generally tends to refuse unfair proposals. In the iterated version of the game, the proposers are able to improve their proposals by adding a value thus making fairer proposals. Such evolutionary aspects are not properly Darwinian-motivated, but they are endowed with a fundamental aspect: they reflect their actions according to value of the offers. Recently, a reactive version of the ultimatum game where acceptance occurs with fixed probability was proposed. In this paper, we aim at exploring this reactive version of the ultimatum game where the acceptance by players depends on the offer. In order to do so, we analyze two situations: (i) mean field and (ii) we consider players inserted within the networks with arbitrary coordination. We then show that the reactive aspect, here studied, thus far not analyzed in the evolutionary game theory literature can unveil an essential feature for the convergence to fifty-fifty split. Moreover we also analyze populations under four different polices ranging from a highly conservative to a moderate one, with respect to decision in changing the proposal based on acceptations. We show that the idea of gaining less more times added to the reciprocity of the players is highly relevant to the "healthy" societies population bargaining concept.
Responder Feelings in a Three-Player Three-Option Ultimatum Game: Affective Determinants of Rejection Behavior  [PDF]
Hans-Rüdiger Pfister,Gisela B?hm
Games , 2012, DOI: 10.3390/g3010001
Abstract: This paper addresses the role of affect and emotions in shaping the behavior of responders in the ultimatum game. A huge amount of research shows that players do not behave in an economically rational way in the ultimatum game, and emotional mechanisms have been proposed as a possible explanation. In particular, feelings of fairness, anger and envy are likely candidates as affective determinants. We introduce a three-player ultimatum game with three-options, which permits the responder to either penalize the proposer or to penalize a third party by rejecting offers. This allows for partially distinguishing rejections due to a retaliation motive driven by anger towards the proposer from rejections due to inequity aversion driven by feelings of envy towards a third party. Results from two experiments suggest that responders experience feelings of dissatisfaction and unfairness if their share is small in comparison to the proposer’s share; anger, then, may trigger rejections towards the proposer. Responders also experience dissatisfaction and envy when third party shares exceed their own shares; however, in contrast to anger, envy does not trigger rejections and is dissociated from the decision to accept or reject an offer. We conclude that acting upon anger is socially acceptable, whereas envy is not acceptable as a reason for action. Furthermore, we find that responders generally feel better after rejections, suggesting that rejections serve to regulate one’s affective state.
Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory  [PDF]
Angel Sanchez,Jose A. Cuesta,Carlos P. Roca
Quantitative Biology , 2005, DOI: 10.1063/1.2008604
Abstract: Human behavior is one of the main problems for evolution, as it is often the case that human actions are disadvantageous for the self and advantageous for other people. Behind this puzzle are our beliefs about rational behavior, based on game theory. Here we show that by going beyond the standard game-theoretical conventions, apparently altruistic behavior can be understood as self-interested. We discuss in detail an example related to the so called Ultimatum game and illustrate the appearance of altruistic behavior induced by fluctuations. In addition, we claim that in general settings, fluctuations play a very relevant role, and we support this claim by considering a completely different example, namely the Stag-Hunt game.
Social Learning in the Ultimatum Game  [PDF]
Boyu Zhang
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0074540
Abstract: In the ultimatum game, two players divide a sum of money. The proposer suggests how to split and the responder can accept or reject. If the suggestion is rejected, both players get nothing. The rational solution is that the responder accepts even the smallest offer but humans prefer fair share. In this paper, we study the ultimatum game by a learning-mutation process based on quantal response equilibrium, where players are assumed boundedly rational and make mistakes when estimating the payoffs of strategies. Social learning is never stabilized at the fair outcome or the rational outcome, but leads to oscillations from offering 40 percent to 50 percent. To be precise, there is a clear tendency to increase the mean offer if it is lower than 40 percent, but will decrease when it reaches the fair offer. If mutations occur rarely, fair behavior is favored in the limit of local mutation. If mutation rate is sufficiently high, fairness can evolve for both local mutation and global mutation.
The Ultimatum Game in Complex Networks  [PDF]
Roberta Sinatra,Jaime Iranzo,Jesús Gómez-Garde?es,Luis M. Floría,Vito Latora,Yamir Moreno
Statistics , 2008, DOI: 10.1088/1742-5468/2009/09/P09012
Abstract: We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an ultimatum game in complex networks. Specifically, three types of players are considered: (a) empathetic, whose aspiration level and offer are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration level and offer are independent. We analyze the asymptotic behavior of pure populations on different topologies using two kinds of strategic update rules. Natural selection, which relies on replicator dynamics, and Social Penalty, inspired in the Bak-Sneppen dynamics, in which players are subjected to a social selection rule penalizing not only the less fitted individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies.
Evolution of Fairness in the Not Quite Ultimatum Game  [PDF]
Genki Ichinose,Hiroki Sayama
Computer Science , 2014,
Abstract: The Ultimatum Game (UG) is an economic game where two players (proposer and responder) decide how to split a certain amount of money. While traditional economic theories based on rational decision making predict that the proposer should make a minimal offer and the responder should accept it, human subjects tend to behave more fairly in UG. Previous studies suggested that extra information such as reputation, empathy, or spatial structure is needed for fairness to evolve in UG. Here we show that fairness can evolve without additional information if players make decisions probabilistically and may continue interactions when the offer is rejected, which we call the Not Quite Ultimatum Game (NQUG). Evolutionary simulations of NQUG showed that the probabilistic decision making contributes to the increase of proposers' offer amounts to avoid rejection, while the repetition of the game works to responders' advantage because they can wait until a good offer comes. These simple extensions greatly promote evolution of fairness in both proposers' offers and responders' acceptance thresholds.
Dynamical spin-glass-like behavior in an evolutionary game  [PDF]
Frantisek Slanina,Yi-Cheng Zhang
Physics , 2000, DOI: 10.1016/S0378-4371(00)00500-8
Abstract: We study a new evolutionary game, where players are tempted to take part by the premium, but compete for being the first who take a specific move. Those, who manage to escape the bulk of players, are the winners. While for large premium the game is very similar to the Minority Game studied earlier, significant new behavior, reminiscent of spin glasses is observed for premium below certain level.
Diversity and critical behavior in prisoner's dilemma game  [PDF]
C. -K. Yun,N. Masuda,B. Kahng
Physics , 2010, DOI: 10.1103/PhysRevE.83.057102
Abstract: The prisoner's dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems consisting of selfish individuals. Here, we study a PD game problem in scale-free networks containing hierarchically organized modules and controllable shortcuts connecting separated hubs. We find that cooperator clusters exhibit a percolation transition in the parameter space (p,b), where p is the occupation probability of shortcuts and b is the temptation payoff in the PD game. The cluster size distribution follows a power law at the transition point. Such a critical behavior, resulting from the combined effect of stochastic processes in the PD game and the heterogeneous structure of complex networks, illustrates the diversity of social relationships and the self-organization of cooperator communities in real-world systems.
Analyzing the payoff of a heterogeneous population in the ultimatum game
Silva, Roberto da;Kellerman, Gustavo Adolfo;
Brazilian Journal of Physics , 2007, DOI: 10.1590/S0103-97332007000800003
Abstract: this paper aims at showing how analytical techniques can be employed to explain the global emerged behavior of a heterogeneous population of ultimatum game players, over different strategies, by calculating their payoff moments. the ultimatum game is a game, in which two players are offered a gift to be shared. one of the players (the proposer) suggests how to divide the offer while the other player (the responder) can either agree or reject the deal. computer simulations were performed considering the concept of turns (in every turn each participant plays necessarily only once, which is equivalent to performing matching a graph) in the game. we reproduce by simulations the expected analytical results at the limit of high number of turns. from these results, we are capable of establishing diagrams to say where each strategy is the best (optimal strategy).
Information in Repeated Ultimatum Game with Unknown Pie Size  [PDF]
Ching Chyi Lee,William K. Lau
Economics Research International , 2013, DOI: 10.1155/2013/470412
Abstract: Within existing literature, it is well known that people’s behavior in ultimatum game experiments cannot be explained by perfect rationality model. There is, however, evidence showing that people are boundedly rational. In this paper, we studied repeated ultimatum game experiments in which the pie size is only known to the proposer (player 1), but the transaction history is made known to both players. We found that subject’s behavior can be very well explained by the history-consistent-rationality model (HCR model) of Lee and Ferguson (2010), which suggests that people’s behavior is affected by what they observed in the past. The HCR model is able to yield point predictions whose errors are on average within 5% of the total pie size. The experimental results provide evidence that subjects' behavior is boundedly rational with respect to the transaction history. 1. Introduction Within the existing ultimatum game literature, it is widely held by economists that game theory fails to predict the subjects' behaviors accurately. Implicit in this evidence are the conjecture of altruistic concerns and the matter of fairness (see, e.g., [1, 2]). While it is commonly known that the decision of accepting or rejecting an offer in ultimatum games depends on respondent's tolerance of unfairness, there have been no prescriptive models in the literature for suggesting the optimal offer that proposer should propose. In this paper, we demonstrate that the history-consistent rationality (hereafter, HCR) model can give point prediction to the proposer's offer in the ultimatum game. This kind of quantitative prediction is different from the past literature which focuses on qualitative prediction. Our research contributions are of twofold. First, our experimental design simulates the real market condition to allow us to better understand how the real economy works. In the existing literatures, scholars have studied ultimatum games with asymmetric information to approximate the real life bargaining situation, as people often do not know how much there is at stake for the other person [3–5]. In our research, we replicate the real market condition by further allowing market information to be available to every subject in the experiment. Consider a person purchasing a house, he would certainly collect market information to bargain for a better deal, because the reservation price of the house owner is usually unknown to the buyer. In each session of our experiments, there are eighteen to twenty pairs of subjects, playing repeated ultimatum games up to twenty periods. The market
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