On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

Evolution of cooperation among mobile agents

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.     

Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter u. Tuning u equal to zero returns the traditional version, while increasing u bears the influence of environment. We find that considering the environment, i.e., integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of u, the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.     

q-Strategy spatial prisoner?s dilemma game

We generalize the usual two-strategy prisoner?s dilemma game to a multi-strategy game, in which the strategy variable s is allowed to take q different fractional values lying between 0 and 1. The fractional-valued strategies signify that individuals are not absolutely cooperative or defective, instead they can adopt intermediate strategies. Simulation results on 1D and 2D lattices show that, compared with the binary strategy game, the multi-strategy game can sustain cooperation in more stringent defective environments. We give a comprehensive analysis of the distributions of the survived strategies and we compare pairwise the relative strength and weakness of different strategies. It turns out that some intermediate strategies survive the pure defection because they can reduce being exploited and at the same time benefit from the spatial reciprocity effect. Our work may shed some light on the intermediate behaviors in human society.     

Evolution of cooperation among mobile agents with heterogenous view radii

In this paper, we study cooperative behavior among mobile agents; the agents have heterogenous view radii and they play the prisoner’s dilemma game with those being within their vision fields. It is found that the cooperation level is remarkably promoted when the heterogeneity of view radii is considered, and the degree distribution of the system is investigated to explain this interesting phenomenon. Moreover, we report that the cooperative behavior is best favored by low density, moderate view radius, and small moving speed. Our findings may be helpful in understanding cooperative behavior in natural and social systems consisting of mobile agents.     

Procedurally Rational Volunteers

The mixed-strategy equilibrium applied to the volunteer's dilemma (Diekmann, 1985 Diekmann , A. ( 1985 ). Volunteer's dilemma . Journal of Conflict Resolution , 29 , 605 – 610 .[Crossref], [Web of Science ®] , [Google Scholar]) predicts that the probability that at least 1 bystander volunteers decreases, if the number of bystander increases. I argue that this prediction lacks empirical support and demonstrate that an alternative solution concept from the literature on bounded rationality, the procedurally rational equilibrium (Osborne &; Rubinstein, 1998 Osborne , M. J. &; Rubinstein , A. ( 1998 ). Games with procedurally rational players . American Economic Review , 88 , 834 – 847 .[Web of Science ®] , [Google Scholar]), yields alternative predictions. I supply some empirical evidence that the alternative solution concept fares better in explaining observed behavior in the volunteer's dilemma.     

Formulation of commons dilemma: Dawes model reconsidered

This paper examines Dawes (1975) model on commons dilemma (CD) situation and proposes an alternative model which formulates CD. Firstly, it makes clear that Dawes model does not have the characteristics of CD. Secondly, it specifies “resource unit condition” which models of commons dilemma must satisfy. Thirdly, it presents CD model, which is obtained by setting the condition in Dawes model. And lastly, it examines some nature of the proposed model and find that in CD situation, fine is distributed proportionally to each player's property.     

一种惩罚机制下一次性n人囚徒困境的合作性

为解决一次性n人囚徒困境中局中人如何走出困境的问题,引进了背叛惩罚函数及其严厉度和参与人的背叛愿意度等概念,并用数学论证法证明了如下结果:(1)参与人的背叛愿意度都不超过1.(2)背叛愿意度越大,这个参与人越愿意背叛;(3)背叛愿意度为0零时,这个参与人是否背叛其赢得一样;(4)当背叛愿意度取负数时,其绝对值越大,参与人的合作积极性越大.得到博弈结果的判定法:(1)计算各参与人的背叛愿意度.(2)若至少有一个参与人愿意背叛,则全体参与人都背叛.(3)若全体参与人都愿意合作,则合作成功.例子表明,本结果在理论上可有效地解决中局中人如何走出困境和在给定惩罚机制下博弈结果的预测问题.     

Prisoner's dilemma and clusters on small‐world networks

The structure of interaction plays an important role in the outcome of evolutionary games. This study investigates the evolution of stochastic strategies of the prisoner's dilemma played on structures ranging from lattices to small world networks. Strategies and payoffs are analyzed as a function of the network characteristics of the node they are playing on. Nodes with lattice‐like neighborhoods tend to perform better than the nodes modified during the rewiring process of the construction of the small‐world network. © 2007 Wiley Periodicals, Inc. Complexity 12:22–36, 2006