Achieving Pareto Optimality in Games via Single-bit Feedback

Abstract: Efficient coordination in multi-agent systems often incurs high communication overhead or slow convergence rates, making scalable welfare optimization difficult. We propose Single-Bit Coordination Dynamics for Pareto-Efficient Outcomes (SBC-PE), a decentralized learning algorithm requiring only a single-bit satisfaction signal per agent each round. Despite this extreme efficiency, SBC-PE guarantees convergence to the exact optimal solution in arbitrary finite games. We establish explicit regret bounds, showing expected regret grows only logarithmically with the horizon, i.e., O(log T). Compared with prior payoff-based or bandit-style rules, SBC-PE uniquely combines minimal signaling, general applicability, and finite-time guarantees. These results show scalable welfare optimization is achievable under minimal communication constraints.