Effect of conformity on evolution of cooperation in a coordination game

Individual decision-making processes are not solely driven by self-interest maximization but are also influenced by the pressure to conform to the group.In primary games like the prisoner's dilemma,the presence of conformity pressure may facilitate the constructive development of cooperative behavior.In this study,we investigate how conformity influences the growth of cooperation in complicated coordination games.Our findings reveal that,even in the presence of stringent game rules,conformity can promote cooperation.In fact,a certain level of conformity pressure can even eliminate the“defection basin”of deer hunting games played on regular networks.Additionally,we demonstrate that the effect of conformity on cooperative behavior is contingent upon the degree of conformity pressure,with different levels of conformity pressure producing opposite effects.These findings provide novel insights into the promotion of cooperative evolution.For instance,if increasing the reward for cooperation has proven ineffective,manipulating the proportion of initial strategy choices may be a more promising approach.

Zero-determinant strategy:An underway revolution in game theory

Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions ac- cording to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant （ZD） strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two play- ers, indicating that a smart player can control her unwitting co-player＇s payoff in a unilateral way [Proc. Acad. Natl. Sci. USA 109, 10409 （2012）]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players, and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis, cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.

THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA

Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed： compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can＇t prevent defection from being evolutionary stable strategy （ESS）. On the other hand, compensation for the coopera- tor can＇t prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.

Influence of Strategy Continuity on Cooperation in Spatial Prisoner’s Dilemma Games with Migrating Players

The phenomenon of cooperation is prevalent in both nature and human society. In this paper a simulative model is developed to examine how the strategy continuity influences cooperation in the spatial prisoner＇s games in which the players migrate through the success-driven migration mechanism. Numerical simulations illustrate that the strategy continuity promotes cooperation at a low rate of migration, while impeding cooperation when the migration rate is higher. The influence of strategy continuity is also dependent on the game types. Through a more dynamic analysis, the different effects of the strategy continuity at low and high rates of migration are explained by the formation, expansion, and extinction of the self-assembled clusters of ＂partial-cooperators＂ within the gaming population.