Evolutionary Game Dynamics On Interdependent Networks

Cooperative behaviors are ubiquitous in the real world. Individuals who choose to cooperate will bring some benefit to others, while pay certain cost at the same time. According to Darwinism that ’the fittest survive’, individuals of low fitness will be eliminated, which means that nature selection does not favor the emergence of cooperation. How to explain the emergence and maintenance of cooperation has received increasing attentions of many scientists with varying research backgrounds. Evolutionary game theory provides a good and effective framework to explore this problem. Meanwhile complex network serves as a useful tool to portray and analyze it. This paper is dedicated to explore the evolution of cooperation on complex network, and the main results are as follows:Firstly, we study the evolutionary competition of several classical strategies, Cooperation, Defection, Tit-for-Tat, and Punishment, in structured populations of finite size. The transition rate between any two strategies is characterized by the corresponding fixation probabilities. By the stochastic process theory, the frequencies that the population resides in each strategy are obtained in the long run. We also explore how the parameters in the payoff matrix influence the evolutionary fate of all strategies. Results show that the introduction of Tit-for-Tat and Punishment strategy can remarkably improve the time fraction of Cooperation in the population, yet still fail to make it predominant over other strategies. In terms of improving Cooperation’s frequency, the situation that Tit-for-Tat and Punishment are present at the same time is not as effective as that when either of them is introduced. In addition, once the fine-cost ratio of Punishment exceeds a certain threshold, nature selection favors Punishment over Tit-for-Tat.Secondly, we develop an original model to explore the evolution of fairness in ultimatum game on interdependent networks. Individuals are separated to proposers and responders, and their roles do not change in the evolutionary process. Proposers and responders are located on two interdependent networks, respectively. They play the ultimatum game according to the interconnectivity. Proposers imitate the strategies of their successful neighbors more likely, while responders self-adjust their strategies according to whether their lowest acceptance levels are satisfied. There is a tradeoff between the rates of these two dynamics. Results show that strong competition can always establish fair giving behavior in the proposer population, while responders follow up their acceptance levels to the egalitarian extend, given that responders down-regulate their unrealized acceptance levels not as low as the proposers’ offers. It is also found that the rate of self-regulating dynamics produces a negligible effect on the eventual population dynamics.