# Fictitious Play with Maximin Initialization

arXiv: https://arxiv.org/abs/2203.10774 · HTML: https://mlsanity.com/paper/2203.10774/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 21 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [Fast Complete Algorithm for Multiplayer Nash Equilibrium](https://mlsanity.com/paper/2002.04734/) (2020)
- [Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games](https://mlsanity.com/paper/2001.11165/) (2020)
- [Computing Nash Equilibria in Multiplayer DAG-Structured Stochastic Games with Persistent Imperfect Information](https://mlsanity.com/paper/2010.13860/) (2020)

## Built on by (most cited first, 2 of 2)

- [Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games](https://mlsanity.com/paper/2509.25618/) (2025)
- [Projected Exploitability Descent for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games](https://mlsanity.com/paper/2606.29169/) (2026)

## Abstract (arXiv)

Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be significantly reduced by carefully selecting the initial strategies. We present several new procedures for strategy initialization and compare them to the classic approach, which initializes all pure strategies to have equal probability. The best-performing approach, called maximin, solves a nonconvex quadratic program to compute initial strategies and results in a nearly 75% reduction in approximation error compared to the classic approach when 5 initializations are used.