# Payoff Performance of Fictitious Play

arXiv: https://arxiv.org/abs/1308.4049 · HTML: https://mlsanity.com/paper/1308.4049/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2013.

## Built on by (most cited first, 4 of 4)

- [Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics](https://mlsanity.com/paper/2301.09619/) (2023)
- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [On the Convergence of Fictitious Play: A Decomposition Approach](https://mlsanity.com/paper/2205.01469/) (2022)
- [Learnable Mixed Nash Equilibria are Collectively Rational](https://mlsanity.com/paper/2510.14907/) (2025)

## Abstract (arXiv)

We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on average or even at all times, and moreover that any game is linearly equivalent to one in which this is the case. Conversely, we provide conditions under which Nash equilibrium payoff dominates fictitious play payoff. A key step in our analysis is to show that fictitious play dynamics asymptotically converges the set of coarse correlated equilibria (a fact which is implicit in the literature).