CHAI researchers Scott Emmons, Andrew Critch, and Stuart Russell published Symmetry, Equilibria, and Robustness in Common-Payoff Games in the Games and Incentives Workshop (GAIW) 2021.

In the paper, the authors show that any locally optimal symmetric strategy profile is also a Nash equilibrium. Applied to machine learning, their result provides a global guarantee for any gradient method that finds a local optimum in symmetric strategy space. They show that this result is robust to perturbations to the common payoff and to the local optimum.