2×2型博弈决策均衡的归一化解法

Normalized Solution for Decision-making Equilibrium of Two-Player-Two-Strategy Typed Game

以往对2×2型博弈求解多使用相对优势划线法、期望支付等值法和最优反应函数法。这些方法存在适用范围有限或过程繁琐的弊端,探求一种普适简便的求解方法具有很强的理论和实践意义。文章在理论上证明,局中人的支付矩阵在局部变换下不改变博弈的均衡特征,并以纳什均衡不变性定理为基础,完成16种2×2型博弈决策均衡的归一化求解。通过产品选择“协调”博弈的算例分析和比较,归一化解法可将复杂的求解过程简单化、程序化和规范化,具有普适性特征,很好地避免了其他方法解的遗漏问题。

For solution of 2 × 2 typed games, we used to employ comparative advantage scoring method, equivalent expecta- tion pay method and optimal reaction function method. Since these methods have such defects as narrow application range or te- dious processes, exploring a simple universal solution is of great theoretical and practical significance. This paper theoretically proves that partial transformation of player＇s payoff matrix does not change equilibrium characteristics of games. Based on Nash equilibrium invariance theorem, the paper completes the normalized solution of 16 kinds of 2 ~ 2 typed game decision-making equilibrium. Finally, through analysis of examples and comparison of product selection coordination, the paper uses normalization method to realize the simplification, routinization and standardization of the complex solution processes, which possesses charac- teristics of universality and nicely avoids omission of using other methods for solution.