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We study the open question of how players learn to play a social optimumpure-strategy Nash equilibrium (PSNE) through repeated interactions ingeneral-sum coordination games. A social optimum of a game is the stablePareto-optimal state that provides a maximum return in the sum of all players'payoffs (social welfare) and always exists. We consider finite repeated gameswhere each player only has access to its own utility (or payoff) function butis able to exchange information with other players. We develop a novel regretmatching (RM) based algorithm for computing an efficient PSNE solution thatcould approach a desired Pareto-optimal outcome yielding the highest socialwelfare among all the attainable equilibria in the long run. Our proposedlearning procedure follows the regret minimization framework but extends it inthree major ways: (1) agents use global, instead of local, utility forcalculating regrets, (2) each agent maintains a small and diminishingexploration probability in order to explore various PSNEs, and (3) agents staywith the actions that achieve the best global utility thus far, regardless ofregrets. We prove that these three extensions enable the algorithm to selectthe stable social optimum equilibrium instead of converging to an arbitrary orcyclic equilibrium as in the conventional RM approach. We demonstrate theeffectiveness of our approach through a set of applications in multi-agentdistributed control, including a large-scale resource allocation game and ahard combinatorial task assignment problem for which no efficient (polynomial)solution exists.

Social Optimum Equilibrium Selection for Distributed Multi-Agent Optimization