Cooperation Research on Zero-Sum Game
The current studies have shown the necessary condition for cooperation is that cost must be less than benefit and there is no cooperation for zero-sum game in which cost is equal to benefit. Here we design a game model of Parrondo’s Paradox in a biological group, which embodies two kinds of game relationships between individual survival and evolution process: 1) the zero-sum game between individuals is called game A. Game A reflects the competition-cooperation relationship between individuals and we set up six kinds of behaviors, such as cooperation, competition, inaction, harmony, matthew and poor-competition-rich-cooperation; 2)the negative-sum game between individuals and environments is called game B. Game B is divided into two branches with different winning probability according to divisibility relations between the total capital and modulus called M. The results of computer simulation and analysis to game A and game B show that: 1) All manner of cooperation and competition behaviors are the adaptive behaviors .2) Harmony behavior has a low social efficiency and lower average fitness of the population, but it is fair and has a high proportion of population viability, equitable distribution of individual fitness.3) Matthew behavior will lead to individual fitness distribution of the population to a extreme imbalance and bring about a Matthew effect which means " Strong individual has always been strong and the weak individual has always been weak". Matthew approach has a lower proportion of the population living. 4) poor-competition-rich-cooperation behavior has the best adaptability, so cooperation of zero-sum game may be carried out by poor-competition-rich-cooperation behavior.
R. Li et al., "Cooperation Research on Zero-Sum Game", Applied Mechanics and Materials, Vols. 44-47, pp. 3338-3344, 2011