Research On Network Game Theory And Man-computer Game Experiments Based On Zero-determinant Strategies

Cooperation has been playing an increasingly vital character in nowadays society,and it is indispensable from the collaboration of cells in organisms,to the coordination of departments in schools and companies,and even to the diplomacy and trade among countries.The investigation of cooperation can help us better understand the intricate phenomena in complex systems and constitute a more harmonious social environment,as well as promoting the coordination within multi-agents and improving the system performance.Game theory has been suggested to provide a unifying framework for studying the cooperation in the competitive context.Although it was traditionally perceived that the payoff of each participant in a game was determined by the players overall,the recently proposed zero-determinant strategies can unilaterally determine the expected payoff relationship of two subjects in a repeated Prisoner’s Dilemma game,which provides a novel perspective on game theory research.Extortion and generosity strategies are two important subsets of zero-determinant strategies.A player adopting extortion strategies can unilaterally ensure her payoff to be not lower than her opponent’s,whereas a player applying generosity strategies can guarantee his payoff is not higher than his opponent’s.These two subsets of strategies have attracted lots of attention.Many realistic complex systems can be characterized by complex networks,such as biological systems,social systems,and the Internet.Through combining complex networks and evolutionary game theory,network evolutionary game theory is aimed at exploring the game interaction and evolutionary dynamics of multi-agents in complex scenarios,which therefore provides a promising approach to understand the collective cooperation in realistic systems.Aside from the theoretical research,game experiment is another important research paradigm of game theory.By conducting experiments,researhers can verify the game theory conclusions,as well as investigating actual behavior rules of individuals,which further provides evidence for the theoretical research.Based on the zero-determinant strategy theory,the current dissertation aims to study the evolution mechanisms of cooperation and the behavioral characteristics of individuals in terms of network evolutionary game theory and man-computer game experiments,respectively.The main contents are summarized as follows:Firstly,we investigate the evolution of extortion as well as its influence on the evolution of cooperation on regular graphs.Based on the repeated Prisoner’s Dilemma game model and the replicator dynamics update rule,we investigate the evolution of cooperation,defection,and extortion strategies on regular graphs by numerical simulation and pairwise approximation.It is revealed that extortion can form stable alliances with cooperation to resist the invasion of defection,and defeat defection on regular graphs eventually,which significantly promote the emergence of cooperation.Subsequently,according to the Fermi function update rule,we find that the level of bounded rationality of individuals plays a non-trivial role on the evolution of cooperation and extortion.Regular graphs are a kind of classical graph models,thus these studies can provide a benchmark for studying game dynamics in more complex structured populations,and have important theoretical value.Secondly,the evolution of extortion strategies on scale-free networks is studied in terms of the repeated Prisoner’s Dilemma game model and the replicator dynamics update rule.We investigate the evolution of cooperation,defection,and extortion on scalefree networks by numerical simulation,and discover that extortion can help cooperation spread from small-degree nodes to large-degree hubs,hence establishs a ”bottom-up”mechanism for the evolution of cooperation.Furthermore,the influence of degree correlation on the evolution is studied,and results show that on assortative networks,extortion can help cooperation occupy the large-degree nodes and resist the invasion of defection through redistributing strategies on networks.However,the assortativity of networks also inhibit cooperation from further diffusion.Previous evidence has shown that the scalefree network model,of which the degree distribution follows a power-law distribution,can efficiently depict the topological properties of realistic systems.Therefore,these studies may inspire new thinking about understanding the emergence of cooperation on realistic networks.Thirdly,the evolution of extortion is explored with the timescale diversity of game interaction and strategy learning being introduced.In the context of imitation rules,there are two kinds of graphs in a network evolutionary game: the interaction graph and the learning graph.Customarily,it is assumed that the two graphs own identical timescale,whereas it may not always be the case.Against this background,we introduce a factor to characterize the level of timescale diversity.It is shown that on regular graphs,proper level of timescale diversity can help cooperators to slow down their update speed while obtaining high payoffs,which paves the way for the emergence of the stable alliances of cooperation and extortion,and thus promotes the overall payoff.Although extortion cannot coexist with cooperation stably on scale-free networks,the interaction of cooperation with extortion can be enhanced on the other hand by introducing timescale diversity,which therefore promotes the frequency of cooperation on networks.These findings may shed lights on better understanding the evolution mechanisms of strategies in realistic contexts.At last,by conducting man-computer experiments based on zero-determinant strategies,we empirically explore subjects’ behavioral performance.Through assigning subjects to play with different categories of zero-determinant strategies as well as informing them the different characteristics of their opponents,we investigate the cooperative behaviors of individuals in game experiments.It is shown that different categories of zerodeterminant strategies have differential influences on individuals’ cooperation during the game,and such difference between the two influences can be moderated by subjects’ knowledge of their opponents’ characteristics.Specifically,precisely informing the subjects that their opponents are computers can efficiently get rid of the inhibiting effect of extortion strategies on cooperation,and on the other hand,reduce the facilitation of generosity strategies on cooperation.In addition,we explore the decision time rules of human subjects,and reveal that in repeated games the subjects’ decision time is heterogeneous,and the distribution has the long-tail phenomenon,which can be fit approximately by a power-law distribution.These conclusions have important values for studying individual cooperation and behavior analysis related to decision time.