Equilibrium Selection in Multi-Agent Policy Gradients via Opponent-Aware Basin Entry

TL;DR

This paper introduces a method to influence which equilibrium multi-agent policy gradients converge to by using opponent-aware basin entry, enhancing cooperative outcomes.

Contribution

It identifies peer-learning correction as a key mechanism for equilibrium selection and proposes annealing to recover standard convergence guarantees.

Findings

Peer-aware updates increase entry into cooperative basins.

The method decomposes into policy gradient plus opponent-aware corrections.

Experiments show improved cooperation in game environments.

Abstract

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.