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.     

Costly punishment and cooperation in the evolutionary snowdrift game

The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character, and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on the initial fractions of the characters, α, β, and the cost-to-benefit ratio r in the SG, the three-character system evolves into a steady state consisting either only of C and P characters or only of C and D characters, in a well-mixed population. The former situation represents an enhancement in cooperation relative to the SG, while the latter is similar to the SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character agents in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P agents is greater than r/β. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population.     

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.     

Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection

We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m$m$-player stopping games and a new kind of m$m$-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided.     

On the cooperation of recycling operations

This paper addresses two important issues that may affect the operations efficiency in the recycling industry. First, the industry contains many small-scale and inefficient recycling firms, especially in developing countries. Second, the output from recycling a waste product often yields multiple recycled products that cannot all be sold efficiently by a single firm. To address these two issues, this paper examines how different firms can cooperate in their recycling and pricing decisions using cooperative game theory. Recycling operations under both joint and individual productions with different cost structures are considered. Decisions include the quantity of waste product to recycle and the price at which to sell each recycled product on each firm’s market. These decisions can be made jointly by multiple cooperating firms to maximize total profit. We design allocation schemes for maximized total profit to encourage cooperation among all firms. Managerial insights are provided from both environmental and economic perspectives.     

On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

Computing approximate Nash equilibria in general network revenue management games

Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.     

时滞系统在博弈中的应用研究

演化博弈理论解决策略均衡问题是目前比较认可的好方法.对于博弈方的经验行为,还未曾研究.本文以非对称2×2的博弈问题为研究对象,建立起带有时滞的博弈系统,通过动力学相关知识,分别研究了两类系统下博弈参与者策略的稳定状态.数值模拟分析了延时给决策带来的影响.实验表明,时滞作用不改变策略的稳定状态,改变的仅是达到稳态的速率.