Equilibrium Selection in Multi-Agent Policy Gradients via Opponent-Aware Basin Entry
For multi-agent reinforcement learning researchers, it provides a theoretical and empirical mechanism for equilibrium selection in policy-gradient methods, though the analysis is limited to finite-unroll settings and specific alignment conditions.
The paper studies equilibrium selection in multi-agent policy gradients, showing that a peer-learning correction term in Meta-MAPG increases the probability of entering a target stable-Nash basin (e.g., cooperative equilibria) compared to ordinary policy gradient. Experiments in Stag Hunt, iterated Prisoner's Dilemma, and neural-policy coordination confirm increased entry into cooperative basins.
Multi-agent policy-gradient methods have been shown to converge locally near stable Nash equilibria. Local convergence, however, does not determine which equilibrium is reached. We study this question through basin-entry probability with respect to a target set of equilibria selected by an external criterion, such as payoff dominance. For finite-unroll Meta-MAPG, we show that the update decomposes into ordinary policy gradient plus own-learning and peer-learning corrections, with controlled sampling noise and finite-unroll bias. We identify the peer-learning correction as the main equilibrium-selection mechanism: under a local alignment condition, the probability of entering the certified attraction region of the target stable-Nash set increases, relative to ordinary policy gradient. Because persistent correction may shift zero-update points of the original game, annealing the correction after entering the basin recovers ordinary policy-gradient dynamics and inherits local stable-Nash convergence guarantees. Experiments in Stag Hunt, iterated Prisoner's Dilemma, and preliminary neural-policy coordination environments support this basin-entry view, showing increased entry into cooperative basins under peer-aware updates.