Cooperation And Phase Diagram In Networked Evolutionary Games

Cooperation is a common phenomenon in human societies and biological systems. However, it is not obvious that there should be cooperation among selfish competitors from the standard point of natural selection. Understanding the emergence of cooperation becomes a fundamental issue. Game theory is a powerful tool to study the basic properties and find principles of rational behavior existing in sociology, biology, economics, and so on. We Study three different game models in this thesis.1)We suggest and study the cooperative behavior of a dissatisfied adaptive prisoner’s dilemma via a pair updating rule. We compare two kinds of relationship among the competing agents, one is the well-mixed population and the other is the two-dimensional square lattice. It is found that the cooperation emerges in both the cases and the frequency of cooperation is enhanced in the square lattice. Though it is impossible for the cooperators to have a higher average payoff than that of the defectors in the well-mixed case, the cooperators in the spatial square lattice could have higher average payoffs in certain regions of the game parameters.2)We study the cooperative behavior and the phase separation in a coevolving system. Agents in the system constructed by a regular random network initially play the snowdrift game with their neighbors. They try to get a better competing environment by imitating neighbor’s more successful strategies or cutting the connection to a defective neighbor and randomly rewiring to another agent in order to seek a better neighborhood. The dynamic process of strategy imitation and relationship among agents due to rewiring neighbors may drive the system into different states.3)We propose and study a dissatisfied adaptive snowdrift game with a payoff pa-rameter r that incorporates a cost for rewiring a connection. An agent, facing adverse local environment, may switch action without a cost or rewire an existing link with a cost a so as to attain a better competing environment. The frequency of cooperation Cf is enhanced(suppressed) at high rewiring cost relative to that at low rewiring cost when r is small(large). For a given value of r, there exists a critical value of the rewiring cost below which the system evolves into a phase of frozen dynamics with isolated noncooperative agents segregated from a cluster of cooperative agents, and above which the system evolves into a connected population of mixed actions with continual dynamics. The phase boundary on the a-r phase space that separates the two phases with distinct structural, population and dynamical properties is mapped out. The phase diagram reveals that, as a general feature, for small r(small a), the disconnected and segregated phase can survive over a wider range of a(r).