The Evolution Of Cooperation And The Demise Of Punishment

Immortal contributions, made by evolutionary biologists Charles Darwin and Martin Nowak, have promoted the sustainable development of the theory of biological evolution in the long history. Charles Darwin’s theory of natural selection, dominated by competition and conflict, has established the widely accepted basic principles of evolution---- mutation and selection. Mutation is involved in the generation of genetic diversity and selection filters out the most environmentally-appropriate individuals. Unfortunately, the theory of natural selection fails to explain the widespread cooperation from lower organisms to human society, and cooperation and competition always seem to exist in opposite ways. With Martin Nowak paying more attention to the inseparable cooperation and competition, like the positive and negative sides of things, the third basic principle of evolution---- cooperation has been proposed. Furthermore, in the freezing competitive environment, more emphasis on the harmony coexistence between cooperation and unmerciful logic of survive has brought out the evolution from genes to organisms, and from languages to complex social behaviors.In recent decades, with numerous evolutionary biologists being fascinated in the exploration of the mechanisms of cooperation evolution, based on their excellent research findings, Martin Nowak has proposed the five rules of cooperation evolution---- kin selection, direct reciprocity, indirect reciprocity, network reciprocity and group selection. Additionally, a unified and simple inequality, which serves to illustrate the conditions of cooperation evolution in the above different mechanisms, has been inducted and generalized.According to the theory of classic direct reciprocity, an extended model of direct reciprocity---- direct reciprocity with costly punishment, has been implemented and researched in this paper. Then, with combination of theoretical analysis and literature review, a "trinity" of the research methods has been established, including the cooperative Nash equilibrium analysis of the extended model, computer simulations and live interactive experiment in finite population.Firstly, in view of the systematic combing of the evolutionary game theory and related literature and deep grasp of the evolution circulation of cooperation and defection, cooperative Nash equilibrium of the direct reciprocity model with costly punishment has been analyzed. And the results showed that, when the cost of costly punishment is not greater than the cost of cooperation, there exists cooperative Nash equilibrium with costly punishment strategy; and the opposite entails the extinct of costly punishment in this model and the cooperative Nash equilibrium is generous titfor-tat.Secondly, this paper has introduced the work of Rand et al.(2009): computer simulations in finite population of direct reciprocity model with costly punishment. Consistency between the results of computer simulations and Nash equilibrium analysis reproduces the statue of cooperation evolution in finite population with random characteristics. However, the results of computer simulations find that, when the cost of costly punishment is not greater than that of cooperation, natural selection will never favor costly punishment within a certain range of parameters, denying the related conclusions of Nash equilibrium analysis.Finally, referring to the live interactive experiments designed by Dreber et al.(2008) and Wu et al.(2009), our live interactive experiments have been designed and carried out in accordance with the direct reciprocity model with costly punishment. And statistical tests and modeling analysis have been implemented for the collected experiment data. Those above analyses fully convinced the conclusions of Nash equilibrium analysis and computer simulations: the evolution of cooperation and the extinct of punishment, determined by the random characteristics of tolerance reflected in the live interactive experiments.