Game Study on the Populational Parrondo's Paradox Based on BA Network

In this article, the author designs a Parrondo's game model of biotic population with the BA scale-free network as its spatial carrier, trying to analyze the individual's competitive and cooperative behaviour. The populational Parrondo's game model includes zero-sum games among individuals and the negative sum-up games between individuals and environment. In terms of zero-sum game relations, four patterns are defined: cooperation, competition, harmony, and Matthew patterns. The simulating calculation result shows that: 1) Cooperation and competition in any form is adaptive behavior. Cooperative and competitive behavior could convert the losing game combination into winning. The positive population average fitness represents the paradoxical feature that the Parrondo's game is counterintuitive. 2) The population average fitness of cooperation and harmony patterns based on BA network is better than that of full connectivity, whereas the average fitness of competition and Matthew patterns is worse than that. BA network is conducive to cooperation. 3) The relationship of individual fitness with node degree and with clustering coefficient is disclosed. As for cooperation pattern, the greater the node degree is, the greater the individual fitness is. In regard to nodes with the same degree, the greater the clustering coefficient is, the smaller the fitness is. For the Matthew pattern, severe polarization of individual fitness turns up, and the "Butterfly Effect" shows.