Study Of Cooperative Behavior In Dynamic Population

Game theory is widely used to study the coopertive behaviors among individuals orgroups. Researchers have often focused on the frequency of cooperation among individualsin the models based on Prisoner's Dilemma game or snowdrift game. As competitivebehavior in real life does not always exist between two agents, the so called N-persongame was proposed to study the cooperation when the game is played by multiple agentssimultaneously. Owing to time payoff, evolutionary N-person Game deserves manyattentions. Scholars found that cooperative behaviors based on Prisoner's Dilemma Gameor Snowdrift Game could be improved in a dynamic system. Following is my main work:Cooperative agents can exist in evolutionary N-person Game in which"self-questioning" mechanism is used. We study agents' behaviors in a two-group systemwhich evolves based on this model. Agents in this system play the game independently ineach group. Also they can move to the other group freely. We find that cooperativebehaviors in the two-group system can be enhanced due to the mobility of agents betweenthe two groups.We propose a model in which we consider the effect of punishment in the ModifiedN-person Game. When the cooperative individuals can punish the defectors in theone-group system by considering the "self-questioning" mechanism, the system mayevolve to an near AllC (all agents are cooperative i.e.,) state at some time. Whilepunishment dose not improve cooperative frequency in the final state when compared tothe system without punishment. Mobility between two-group system can make the twogroups be in the AllC state quickly. However, low power punishment in the one groupsystem with "imitation" mechanism may lead the system to be in an AllC state or in anAllD (all agents are defectors i.e.,) state-it depends on the initial state of the group. AllCstate may exist in such a group when the power of punishment is raised. We find the theory based on the voting model suggested by Federico Vazquez can notexplain the simulation result quite well. We discard the node neighbours' binomialdistribution and suggest a new distribution. We analyze the statistical behaviorstheoretically and calculate the critical point where the dynamic opinion links disappear.Our theoretical result fits well to the simulation result.