Indirect Reciprocity, Costly Punishment And The Evolution To Social Cooperation

Cooperation is of utmost importance of human society, and it is the base of our civilization.Social cooperation refers to the social state that individuals tend to incur own cost to make ahigher social benefit in a society with large amount of individuals. With the expanding of thescope of everyday life and the elaboration of labor division and specialization, one has morechance to interact with strangers, and the cooperation of strangers in society with a large scale ofpopulation is referred to as indirect reciprocity. How does indirect reciprocity emerge amongselfish individuals? Recently, costly punishment which means that punisher incurs a cost to makea loss to the punished draws much attention. But the role of costly punishment in promotingcooperation is ambiguous, such as Ohtsuki etc. found that costly punishment will decrease thesocial benefit in the cooperative evolutionary stable state.This paper studies the role of costly punishment in promote social cooperation of indirectreciprocity comprehensively using the methods of population dynamics, live interactiveexperiments and agent-based simulation. Individuals may adopt different kinds of strategieswhich may be cooperative or not cooperative and may use or do not use punishment. Individualsadopting different kinds of strategies are analogical to different populations in ecological system,and the expected revenue of a strategy is its fitness in evolution. Population dynamics is used tomodel the evolution of the distribution of all strategies which determines the level of socialcooperation and the tendency to punish. By live interactive experiments, subjects are recruited tointeract with each other in a virtual society, which can provide the direct and reliable individualbehavioral pattern and social evolution route. By multi-agent simulation, we can model thebehavior pattern of each individual and investigate how interaction of individual can generatehigh level phenomenon. Multi-agent simulation can provide the underlying mechanism for theevolution of social cooperation.Firstly, we study the role of punishment in the route of social cooperation evolution. Theevolution dynamic of individuals' strategies is explicitly modeled. We find that costlypunishment can enlarge the attraction basin of cooperative social states which implies that asociety can only struggle out of social dilemma by using punishment if there are too manyno-cooperators and increase the converge rate to cooperative state which implies that punishment can make a society speed up to a more cooperative state if the society is not patient enough. Liveinteractive experiments based on this model support the theoretical results. Form a state with fewcooperators, the cooperation ratio increases rapidly in a society encouraging punishment whilethe cooperation ratio decreases in a society not encouraging punishment. Agent-based simulationreplicates the results of theoretical analysis and provides the underlying mechanism ofcooperation evolution. The influence of society population size, individual learning rate andindividual memory length is also analyzed.Secondly, we study the role of costly punishment in a society with birth-death mechanism.In model above, punishment only works in the route to cooperation, and it will decrease thesocial benefit in the stable state. Then why punishment still prevails after so long history ofevolution? We introduce the birth-death mechanism which assumes that old individuals will exitand new individuals will enter. The exiting are those who adapted to the society and cooperate,while the newcomers are inherently selfish and defect. We model and analyze the evolution ofstrategy distribution as population dynamics. It is found that the effect of costly punishment ismore significant in society with birth-death mechanism; and punishment can provide the highersocial benefit even in the stable state of social evolution.Lastly, we study the role of costly punishment in a society with no reputation mechanism.The models above are based on perfect reputation mechanism and the action of each individual isobserved and is assigned a reputation public to all. The discriminating treatment to differentreputation leads to the indirect reciprocity. Can social cooperation be maintained in a societywith no reputation mechanism? We find that a society can accomplish some extent ofcooperation without reputation mechanism with the help of punishment and power asymmetry.Individuals can choose to be police or citizen. A police has a duty to punish a defector whenencountering while enjoys a privilege to get less punishment when he defects to another police.The privilege provides the incentive of small part of individuals to be police and the existence ofpunishment deters most individuals to cooperate. This makes a corruptive social cooperationcomposed of cooperative citizen and nocooperative police. We also find that the effect of costlypunishment and power asymmetry is more significant when there are many defectors in a societyand too large power asymmetry will lead to severe corruption and decrease the social benefitwhen there are already many cooperators.