For Learning in Symmetric Teams, Local Optima are Global Nash Equilibria. (arXiv:2207.03470v1 [cs.GT])

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 …

arxiv equilibria global learning