Exploring Evolutionary Games On Complex Networks

Coupled biological and ecological systems, social interacting species, economic agents, are typical examples of systems composed by a large number of highly interconnected dynamical units. The global properties of such complex systems can be modeled by complex networks whose nodes represent the dynamical units, and whose links stand for the interactions between them. The emergence and abundance of cooperation in these systems poses a tenacious and challenging puzzle to evolution theory. In this thesis, we explore evolutionary prisoner's dilemma games on complex networks and address how the evolution of cooperation is affected by the network topology, and also search for new mechanisms supporting the emergence and persistence of cooperation.First, motivated by aging phenomenon of individuals of real complex systems, a weight-dependent deactivation model generating networks with high clustering coefficient is proposed to model evolving networks. We determine the degree distribution of the generated networks by master-equation approach complemented by Monte-Carlo simulation. Both analytical solutions and numerical simulations show that the generated networks possess strong structural effect. Weighted, structured scale-free networks are obtained as the deactivated vertex is target selected at each time step, and weighted, structured exponential networks are realized for the random-selected case.In the second, a modified spatial PDG with voluntary participation in Newman-Watts small-world networks is studied. Each agent in the network is a pure strategist and can only take one of three strategies: cooperate, defect and loner; its strategical transformation is associated with both the number of current strategical states and the magnitude of average profits of the involved players; a stochastic strategy mutation is applied when it gets into the trouble of local commons. In the case of very low temptation to defect, it is found that agents are willing to participate in the game in typical small-world region and intensive collective oscillations arise in more random region.Thirdly, we incorporate a dynamic (or static) preferential selection (DPS) mechanism into an evolutionary PDG and reveal a new mechanism for maintaining cooperation. By considering asymmetric and heterogeneous influential effects in many natural populations, we define impact weights for any pairs of neighboring individuals, which describes the influence of one player on another and evolves promptly. Based on this quantity, a DPS mechanism is introduced into the dynamics: the more influential a neighbor is, the greater probability it is picked as a reference. We find that the DPS gives rise to very large broad distributions of the impact weights, which favors the influential cooperators to form stable communities, and thereby prevents the invasion from defectors, hence contributes to the emergence and persistence of cooperation.Fourthly, in order to investigate the influence of heterogeneous interaction neighborhood on the evolution of cooperation, we study an evolutionary PDG with players located on Barabasi-Albert scale-free networks with different update rules that determine a player's future strategy. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced by the scale-free topology. The differences depend on the detailed evaluation function of the players' success, the different update rules that determine a player's future strategy, the synchronous and asynchronous events of strategy-updating, and also on the magnitude of the temptation to defect.Finally, we study an evolutionary PDG with two layered graphs, where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy learning mechanism. This system is investigated by means of Monte Carlo simulations as well as an extended pair-approximation method. We consider the average density of cooperators in the stationary state for fixed interaction graph, while varying the number of edges in the learning graph. According to the Monte Carlo simulations, the cooperation is modified substantially in a way resembling a coherence-resonance-like behavior when the number of learning edges is increased. Too little learning information favors defection, but apparently so does too much information. The optimal enhancement is induced by moderate difference between the interaction and learning neighborhoods.