# Convergence of Monte Carlo Tree Search in Simultaneous Move Games

arXiv: https://arxiv.org/abs/1310.8613 · HTML: https://mlsanity.com/paper/1310.8613/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2013.

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

- [Mastering Zero-Shot Interactions in Cooperative and Competitive Simultaneous Games](https://mlsanity.com/paper/2402.03136/) (2024)
- [PokaiTrainer: Scaling Equilibrium Search to Competitive Pok'emon VGC](https://mlsanity.com/paper/2608.29197/) (2026)

## Abstract (arXiv)

We study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with perfect information and simultaneous moves. We present a general template of MCTS algorithms for these games, which can be instantiated by various selection methods. We formally prove that if a selection method is ε-Hannan consistent in a matrix game and satisfies additional requirements on exploration, then the MCTS algorithm eventually converges to an approximate Nash equilibrium (NE) of the extensive-form game. We empirically evaluate this claim using regret matching and Exp3 as the selection methods on randomly generated games and empirically selected worst case games. We confirm the formal result and show that additional MCTS variants also converge to approximate NE on the evaluated games.