Abstract: With the increase of the number of people in a game, it is very difficult to use the traditional “dominant” methods and “valuation” methods to solve the cooperative game whether in logic or calculation. To solve this problem, the solution of cooperative game is regarded as an interactive and convergent process. According to the effectiveness and individual rationality, the game players put forward the allocation scheme and adjust them to be consistent. On the basis of this viewpoint, the cooperative game model based on particle swarm optimization(PSO)is constructed, all players are equal to particle swarm, the interactive strategy of the players are mapped into fitness function, meanwhile the interaction and convergence of the players are mapped into the calculation process of the particle swarm optimization algorithm, and the parameters in the velocity formula are set. Through the analysis of an example, the particle swarm optimization algorithm has the characteristics of fast convergence, high precision and easy realization, and players can quickly and easily get the unique solution of the cooperative game by using this method. This paper can be used as a reference for solving cooperative games, and will provide a new method and a tool for decision makers to use the cooperative game theory.

Key words: particle swarm optimization algorithm, cooperative game solution, individual rationality

摘要： 随着局中人人数的增加,利用传统的“占优”方法和“估值”方法进行合作博弈求解无论从逻辑上还是计算上都变得非常困难。针对此问题,将合作博弈的求解看作是局中人遵照有效性和个体理性提出分配方案,并按照一定规则不断迭代调整直至所有方案趋向一致的过程。依据该思路,对合作博弈粒子群算法模型进行构建,确定适应度函数,设置速度公式中的参数。通过算例分析,利用粒子群算法收敛快、精度高、容易实现的特点,可以迅速得到合作博弈的唯一分配值,这为求解合作博弈提供了新的方法和工具。

关键词: 粒子群算法, 合作博弈, 个体理性