A Liapunov Function for Nash Equilibria

Abstract

In this paper, I construct a Liapunov function for Nash equilibria for finite n–person games in normal form. This function is useful for computation of Nash equilibria, since it converts the problem into a standard minimization problem. It provides an alternative to existing computational methods, which are based either on n - person extensions of the algorithm of Lemke and Howson [1961] (eg., Wilson [1971] and Rosenmiiller [1971]), or on methods for finding the fixed point of the best response correspondence, such as simplicial division algorithms (eg., Todd [1976], and Van der Laan et al. [1987]). This work is also related to that of Brown and von Neumann [1950], and Rosen [1964], who construct differential equation systems for solving certain classes of games.

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