Research On The Probability Of Cooperation In The Prisoner’s Dilemma Game

Prisoner’s dilemma has reflected some social problems in reality, and the cooperative behavior in the game can help resolve social dilemma. However, traditional game theory suggests that rational people will only choose non-cooperative behavior in prisoner’s dilemma games. The mechanism of cooperative behavior is still unclear and the probability that people choose cooperation is inconstant. Experts advocate cooperation to realize the win-win situation, but the advocacy often fails without an effective mechanism design. So far the research on the model of cooperation probability in prisoner’s dilemma is little. To improve the probability that people choose cooperation, we should quantify each influence factor so as to optimize the mechanism design accordingly. This paper researches on the probability of cooperation in prisoner’s dilemma game and establishes the mathematic model which can be used for quantitative analysis for mechanism optimization.Considering that interest is the most fundamental factor that affects participants’ decisions, this paper conducts correlation analysis between the payoffs in the game matrix and the cooperation strategy for the first time, and further explores each payoff ’s influence extent. Besides interest, this paper also takes the participants’ heterogeneity and game mutuality into account to establish the probability model of cooperation. We use the experimental data provided by Butler(2012) to verify the model and conduct nonlinear regression analysis to test the goodness of fit. The model is simple and flexible, which conforms to the decision making characteristics and elaborative faculty of human beings.Besides that, this paper conducts research on the probability of team reasoning which is one of the motivational factors used to explain the cooperative behavior in prisoner’s dilemma. People who act in the team reasoning mode seek for the best actions for the whole rather than self-interest. Based on the probability model of team reasoning put forward by Smerilli(2012), this paper deduces the specific transition function to complete the model and applies it to the mechanism design of interest allocation. We establish the linear transition model and analyze the interest allocation method to maximize the probability of team reasoning. Then the research is extended to nonlinear transition model and discusses the design of allocation mechanism when the transition function is convex or concave, respectively. Also, the model has been verified through behavioral experiment, including symmetric and asymmetric prisoner’s dilemma games.