Smooth Fictitious Play in $N\times 2$ Potential Games

TL;DR

This paper proves that smooth fictitious play converges to near a pure Nash equilibrium in almost all N×2 potential games, with the neighborhood size controllable by the smoothing parameter, using simple proof methods.

Contribution

It establishes convergence properties of smooth fictitious play in N×2 potential games and introduces straightforward proof techniques for regular potential games.

Findings

Convergence to a neighborhood of Nash equilibrium with probability 1

Neighborhood size can be made arbitrarily small

Applicable to almost all N×2 potential games

Abstract

The paper shows that smooth fictitious play converges to a neighborhood of a pure-strategy Nash equilibrium with probability 1 in almost all $N\times 2$ ($N$-player, two-action) potential games. The neighborhood of convergence may be made arbitrarily small by taking the smoothing parameter to zero. Simple proof techniques are furnished by considering regular potential games.