Noncooperative multi-agent systems often face coordination challenges due to conflicting preferences among agents. In particular, when agents act in their own self-interest, they may prefer different choices among multiple feasible outcomes, leading to suboptimal outcomes or even safety concerns. We propose an algorithm named trading auction for consensus (TACo), a decentralized approach that enables noncooperative agents to reach consensus without communicating directly or disclosing private valuations. TACo facilitates coordination through a structured trading-based auction, where agents iteratively select choices of interest and provably reach an agreement within an a priori bounded number of steps. A series of numerical experiments validate that the termination guarantees of TACo hold in practice, and show that TACo achieves a median performance that minimizes the total cost across all agents, while allocating resources significantly more fairly than baseline approaches.

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