混合策略纳什均衡的新教法

A Novel Approach to Teach Mixed Strategy Nash Equilibrium

理解博弈论中的最优混合策略对本科生而言具有一定困难,而目前教材中对此内容的讲述又过于抽象.提出一个简单而有效地讲授混合策略纳什均衡的方法.首先利用猜硬币游戏引入并介绍混合策略的基本该念.再通过将混合策略加入到支付矩阵中构造拓展支付矩阵,使学生可以清晰地看到采用混合策略的结果,实现从纯策略到混合策略的自然过渡.然后引导学生思考博弈参与者采用混合策略的各种动机,并在拓展支付矩阵中检验其是否达成均衡.最后介绍最优混合策略计算的一般方法,并分析其与参与者行为动机之间的一致性.课堂实践证明,方法可以有效提高学生对混合策略纳什均衡的综合理解,学生不仅能够更好地掌握求解技术,而且能更深入地理解其经济学含义.

It is difficult for undergraduate students to understand the mixed strategy nash equilibrium in game theory. At the same time, the description to this part in most current textbooks is too abstract. This paper presents a novel approach which is easy-executing and efficient. Firstly, students are asked to play a simple pennies matching game and the basic conceptions are introduced based on this game. And we introduce a extended payoff matrix which includes a new row and a new column with mixed strategy, this makes the students clearly see the results of employing mixed strategies. Then the students are guided to consider the possible motivations of players to mix their strategy and verify which incentive can make the game in equilibrium based on the extended payoff matrix. Lastly, a general method is introduced to calculate the mixed strategy nash equilibrium, and its consistence with the players＇ incentive is analyzed. Classroom experience shows that this approach improves the students＇ comprehension of mixed strategies, they not only can grasp the calculation techniques better, but also can understand the economic intuition deeper.