# Entropy-Regularized Stochastic Games

arXiv: https://arxiv.org/abs/1907.11543 · HTML: https://mlsanity.com/paper/1907.11543/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization](https://mlsanity.com/paper/2105.15186/) (2021)
- [Robust Adversarial Reinforcement Learning via Bounded Rationality Curricula](https://mlsanity.com/paper/2311.01642/) (2023)
- [Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods](https://mlsanity.com/paper/2301.13006/) (2023)
- [Unified Policy Optimization for Continuous-action Reinforcement Learning in Non-stationary Tasks and Games](https://mlsanity.com/paper/2208.09452/) (2022)
- [Continuous-Time Reinforcement Learning for N-Player Stochastic Differential Games with Exploratory Policies](https://mlsanity.com/paper/2607.19928/) (2026)

## Abstract (arXiv)

In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have perfect information about the stochastic transition model of the environment. However, implementing such strategies may make the players vulnerable to unforeseen changes in the environment. In this paper, we introduce entropy-regularized stochastic games where each player aims to maximize the causal entropy of its strategy in addition to its expected payoff. The regularization term balances each player's rationality with its belief about the level of misinformation about the transition model. We consider both entropy-regularized N-stage and entropy-regularized discounted stochastic games, and establish the existence of a value in both games. Moreover, we prove the sufficiency of Markovian and stationary mixed strategies to attain the value, respectively, in N-stage and discounted games. Finally, we present algorithms, which are based on convex optimization problems, to compute the optimal strategies. In a numerical example, we demonstrate the proposed method on a motion planning scenario and illustrate the effect of the regularization term on the expected payoff.