Fictitious Play with Maximin Initialization

TL;DR

This paper demonstrates that initializing fictitious play with maximin strategies significantly reduces equilibrium approximation error in multiplayer games, offering a novel initialization method that outperforms traditional uniform strategies.

Contribution

Introduces a maximin-based initialization procedure for fictitious play, substantially improving approximation accuracy in multiplayer game equilibrium computations.

Findings

Maximin initialization reduces approximation error by up to 75%.

The proposed method outperforms classic uniform initialization.

Nonconvex quadratic programming is used for strategy computation.

Abstract

Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be significantly reduced by carefully selecting the initial strategies. We present several new procedures for strategy initialization and compare them to the classic approach, which initializes all pure strategies to have equal probability. The best-performing approach, called maximin, solves a nonconvex quadratic program to compute initial strategies and results in a nearly 75% reduction in approximation error compared to the classic approach when 5 initializations are used.