Abstract: Considering the assigned persons' individual rationality, this paper proposed the a method to solve the assignment problem with game theory, and prove the existence of the pure strategy nash equilibrium. Compare with the assignment result, the Pure Strategy Nash Equilibrium correspond Pareto Optimum. And it is the optimal solution in individual rational environment. Above all, we proposed a complex method considering individual rationality and group rationality simultaneously.

Key words: the assignment problem, the nash equilibrium, individual rationality

摘要： 为弥补传统指派问题解不符合个体理性的不足,提出指派问题的纳什均衡解,并证明有限指派问题有且仅有纯纳什均衡解。相比传统的指派问题解,纯纳什均衡符合Pareto最优,是个体理性视角下的最优解。在此基础上,给出一个综合考虑个体理性与集体理性的求解方法。

关键词: 指派问题, 纳什均衡, 个体理性