GAME-MODEL RESEARCH ON COOPETITION BEHAVIOR OF PARRONDO'S PARADOX BASED ON NETWORK

Abstract

The paper devises a Parrondo's game model of biotic population with the network as its spatial carrier, trying to analyze individual's coopetition behavior and investigate the degree distribution of the heterogeneity on the impact of coopetition. The populational Parrondo's game model consists of a zero-sum game among individuals and a negative sum game between individuals and environment. In terms of relations of zero-sum game, four patterns are defined: cooperation, competition, harmony, and poor-competition-rich-cooperation. The simulation result shows that: (1) Cooperation and competition in any forms are adaptive behaviors. Cooperative and competitive behavior could convert the losing games combined into winning. The positive average fitness of the population represents the paradoxical feature that the Parrondo's game is counterintuitive. (2) BA Network is conducive to cooperation. (3) The relationships of individual fitness with node degree and with clustering coefficient are disclosed. As for cooperation and poor-competition-rich-cooperation pattern, the greater the node degree is, the greater the individual fitness is. (4) The heterogeneity has a positive impact on cooperation. (5) Population average fitness is the largest when the probability of playing zero-sum game is 1/3 in the Parrondo's game model.