# Intelligent Players in a Fictitious Play Framework

arXiv: https://arxiv.org/abs/2110.05939 · HTML: https://mlsanity.com/paper/2110.05939/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Strategizing against Q-learners: A Control-theoretical Approach](https://mlsanity.com/paper/2403.08906/) (2024)
- [Optimistic Regret Bounds for Online Learning in Adversarial Markov Decision Processes](https://mlsanity.com/paper/2405.02188/) (2024)
- [Omniscient Attacker in Stochastic Security Games with Interdependent Nodes](https://mlsanity.com/paper/2512.04561/) (2025)

## Abstract (arXiv)

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.