Consistency of vanishing smooth fictitious play

TL;DR

This paper investigates the long-term behavior of Vanishing Smooth Fictitious Play, a game-theoretic strategy with a decreasing smoothing parameter, addressing an open question about its consistency.

Contribution

It provides a theoretical analysis confirming the consistency of Vanishing Smooth Fictitious Play as the smoothing parameter diminishes over time.

Findings

Establishes the conditions under which the strategy is consistent.

Answers an open question posed by Fudenberg and Takahashi.

Contributes to understanding the convergence properties of smooth fictitious play.

Abstract

We discuss consistency of Vanishing Smooth Fictitious Play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothing parameter is time-dependent and asymptotically vanishes. This answers a question initially raised by Drew Fudenberg and Satoru Takahashi.