基于连续同伦的多方对策之Nash均衡点的机械化求解方法

A Mechanical Method for Computing the Nash Mixed Equilibrium via Continuous Homotopy

Nash定理证明非合作n人矩阵对策一定有混合平衡解,现有文献多讨论n=2时混合平衡解的求法,一般用优化或逼近的方法.文章给出了一种机械化求解方法,通过构造非合作多人矩阵对策的混合平衡局势所满足的多项式方程组,应用方程组求解软件由此可直接求出多人对策的问题的各种混合平衡解.

Applying the Brouwer fixed theorems Nash proved that there exists at least one mixed equilibrium point for any n-player non-cooperative game.For solving the mixed equilibrium of given games,most of previous works in literatures as we know are designed for 2-player zero-sum or non-zero-sum cases,and the methods are mainly based on numerical optimization or approximate computation.In this paper,we present an innovative mechanical method to construct polynomial equations for Nash mixed equilibrium points,therefore combining the continuous homotopy method one can find all mixed equilibria directly.