Abstract: In case where there is a competition among the sources(warehouses or suppliers)or destinations(demand points or consumers), in this situation, using the traditional method to solve the problem may be seen as undesirable and unfair. Specifically, each source or destination is viewed as a player that seeks to maximize its own efficiency or minimize its own cost. To address this issue, the transportation problem is solved with the game theory in the first time, and its Nash equilibrium and Nash bargaining solution is proposed. The virtual transportationproblem in the non-cooperate situation is the assignment that each person pursues the most efficient task to his own benefit. Most importantly, the Nash equilibrium of the assignment problem is also the Nash equilibrium of the transportation problem. Based on the Nash equilibrium of the transportation problem, the Nash bargaining model of the transportation problem is proposed, and it is showed that the optimal solution constitutes a Nash bargaining solution with experiments. Because the Nash bargaining model may have more than one solution, we propose an evaluation method to calculate the decision maker’s expected monitoring cost. Finally, its Shapely value is discussed.

Key words: transportation problem, game, nash equilibrium, nash bargaining solution, shapely value

摘要： 产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。

关键词: 运输问题, 博弈论, 纳什均衡, 纳什讨价还价解, Shapely值