论文标题
复杂游戏理论简介
An Introduction to Complex Game Theory
论文作者
论文摘要
关于两人零和游戏的已知结果自然在复杂空间中概括，并通过完整的紧凑理论提出。收益功能是由实际情况下的回报功能的实际部分定义的，纯复杂策略由凸polytope $s_α^m的极端点来定义$α$ in $（0，\fracπ{2}）e $。这些策略允许有关NASH平衡，玩家的安全水平及其关系的定义和结果，以$ \ Mathbb {C}^{M} $扩展。给出了在复杂空间中的最小值定理的新的建设性证明，这表明了一种精确计算两个玩家零和复杂游戏的平衡的方法。还获得了基于表单$ bz = b $的复杂线性系统的解决方案的一种简单解决方案方法。
The known results regarding two-player zero-sum games are naturally generalized in complex space and are presented through a complete compact theory. The payoff function is defined by the real part of the payoff function in the real case, and pure complex strategies are defined by the extreme points of the convex polytope $S_α^m:=\{z\in\mathbb{C}^m:$ $|argz|\leqqα,\;\sum_{i=1}^{m}z_i=1\}$ for "strategy argument" $α$ in $(0,\fracπ{2})e$. These strategies allow definitions and results regarding Nash equilibria, security levels of players and their relations to be extended in $\mathbb{C}^{m}$. A new constructive proof of the Minimax Theorem in complex space is given, which indicates a method for precisely calculating the equilibria of two-player zero-sum complex games. A simpler solution method of such games, based on the solutions of complex linear systems of the form $Bz=b$, is also obtained.
