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

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