Intelligent Players in a Fictitious Play Framework

TL;DR

This paper explores how an intelligent player with full payoff knowledge can outperform Nash equilibrium strategies in a fictitious play setting, revealing vulnerabilities in the classical learning algorithm.

Contribution

It demonstrates that an intelligent player can exploit fictitious play by deviating from its assumptions to gain higher payoffs, highlighting a fragility in the algorithm.

Findings

Intelligent players can outperform Nash equilibrium in fictitious play.

Deviating from fictitious play can lead to better payoffs for strategic players.

Fictitious play is vulnerable to strategic exploitation.

Abstract

Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the game. We consider the presence of an intelligent player that has access to the entire payoff matrix for the game. We show that by not conforming to fictitious play, such a player can achieve a better payoff than the one at the Nash Equilibrium. This result can be viewed both as a fragility of the fictitious play algorithm to a strategic intelligent player and an indication that players should not throw away additional information they may have, as suggested by classical fictitious play.