Learning by Fictitious Play in Large Populations

TL;DR

This paper models fictitious play learning in large populations using a mean-field approach, analyzing its qualitative properties and asymptotic behavior, and comparing effects of memory factors.

Contribution

It introduces a mean-field model for fictitious play in large populations and connects it to continuous best-response dynamics, highlighting the impact of memory.

Findings

Model converges to continuous best-response dynamics

Memory factor influences learning stability

Asymptotic behavior aligns with theoretical predictions

Abstract

We consider learning by fictitious play in a large population of agents engaged in single-play, two-person rounds of a symmetric game, and derive a mean-filed type model for the corresponding stochastic process. Using this model, we describe qualitative properties of the learning process and discuss its asymptotic behavior. Of the special interest is the comparative characteristics of the fictitious play learning with and without a memory factor. As a part of the analysis, we show that the model leads to the continuous, best-response dynamics equation of Gilboa and Matsui (1991), when all agents have similar empirical probabilities.