# For Learning in Symmetric Teams, Local Optima are Global Nash Equilibria

arXiv: https://arxiv.org/abs/2207.03470 · HTML: https://mlsanity.com/paper/2207.03470/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 7 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Cooperative Inverse Reinforcement Learning](https://mlsanity.com/paper/1606.03137/) (2016)
- [RoboNet: Large-Scale Multi-Robot Learning](https://mlsanity.com/paper/1910.11215/) (2019)
- ["Other-Play" for Zero-Shot Coordination](https://mlsanity.com/paper/2003.02979/) (2020)
- [A New Formalism, Method and Open Issues for Zero-Shot Coordination](https://mlsanity.com/paper/2106.06613/) (2021)
- [On the Characterization of Local Nash Equilibria in Continuous Games](https://mlsanity.com/paper/1411.2168/) (2014)
- [Computational Results for Extensive-Form Adversarial Team Games](https://mlsanity.com/paper/1711.06930/) (2017)
- [Public Information Representation for Adversarial Team Games](https://mlsanity.com/paper/2201.10377/) (2022)

## Built on by (most cited first, 7 of 7)

- [Efficiently Computing Nash Equilibria in Adversarial Team Markov Games](https://mlsanity.com/paper/2208.02204/) (2022)
- [Learning Equilibria in Adversarial Team Markov Games: A Nonconvex-Hidden-Concave Min-Max Optimization Problem](https://mlsanity.com/paper/2410.05673/) (2024)
- [Imperfect-Recall Games: Equilibrium Concepts and Their Complexity](https://mlsanity.com/paper/2406.15970/) (2024)
- [Computing Game Symmetries and Equilibria That Respect Them](https://mlsanity.com/paper/2501.08905/) (2025)
- [Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property](https://mlsanity.com/paper/2312.12067/) (2023)
- [Markov Potential Game and Multi-Agent Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/2603.19188/) (2026)
- [Decision Making under Imperfect Recall: Algorithms and Benchmarks](https://mlsanity.com/paper/2602.15252/) (2026)

## Abstract (arXiv)

Although it has been known since the 1970s that a globally optimal strategy profile in a common-payoff game is a Nash equilibrium, global optimality is a strict requirement that limits the result's applicability. In this work, we show that any locally optimal symmetric strategy profile is also a (global) Nash equilibrium. Furthermore, we show that this result is robust to perturbations to the common payoff and to the local optimum. Applied to machine learning, our result provides a global guarantee for any gradient method that finds a local optimum in symmetric strategy space. While this result indicates stability to unilateral deviation, we nevertheless identify broad classes of games where mixed local optima are unstable under joint, asymmetric deviations. We analyze the prevalence of instability by running learning algorithms in a suite of symmetric games, and we conclude by discussing the applicability of our results to multi-agent RL, cooperative inverse RL, and decentralized POMDPs.