# Playing Markov Games Without Observing Payoffs

arXiv: https://arxiv.org/abs/2509.00179 · HTML: https://mlsanity.com/paper/2509.00179/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transition](https://mlsanity.com/paper/2006.05606/) (2020)
- [Breaking the Curse of Multiagents in a Large State Space: RL in Markov Games with Independent Linear Function Approximation](https://mlsanity.com/paper/2302.03673/) (2023)
- [Regret Minimization and Convergence to Equilibria in General-sum Markov Games](https://mlsanity.com/paper/2207.14211/) (2022)
- [Learning Markov Games with Adversarial Opponents: Efficient Algorithms and Fundamental Limits](https://mlsanity.com/paper/2203.06803/) (2022)
- [Near-Optimal Policy Optimization for Correlated Equilibrium in General-Sum Markov Games](https://mlsanity.com/paper/2401.15240/) (2024)
- [O(T-1) Convergence of Optimistic-Follow-the-Regularized-Leader in Two-Player Zero-Sum Markov Games](https://mlsanity.com/paper/2209.12430/) (2022)
- [An Online Convex Optimization Approach to Blackwell's Approachability](https://mlsanity.com/paper/1503.00255/) (2015)
- [Satisficing Paths and Independent Multi-Agent Reinforcement Learning in Stochastic Games](https://mlsanity.com/paper/2110.04638/) (2021)

## Abstract (arXiv)

Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated symmetric two-player matrix games without observing payoffs, as long as the opponents actions are observed. In this paper, we introduce and formalize a new class of zero-sum symmetric Markov games, which extends the notion of symmetry from matrix games to the Markovian setting. We show that even without observing payoffs, a player who knows the transition dynamics and observes only the opponents sequence of actions can still compete against an adversary who may have complete knowledge of the game. We formalize three distinct notions of symmetry in this setting and show that, under these conditions, the learning problem can be reduced to an instance of online learning, enabling the player to asymptotically match the return of the opponent despite lacking payoff observations. Our algorithms apply to both matrix and Markov games, and run in polynomial time with respect to the size of the game and the number of episodes. Our work broadens the class of games in which robust learning is possible under severe informational disadvantage and deepens the connection between online learning and adversarial game theory.