Decentralized and Uncoordinated Learning of Stable Matchings: A Game-Theoretic Approach

• URL: http://arxiv.org/abs/2407.21294v2
• Date: Thu, 15 Aug 2024 02:57:09 GMT
• Title: Decentralized and Uncoordinated Learning of Stable Matchings: A Game-Theoretic Approach
• Authors: S. Rasoul Etesami, R. Srikant,
• Abstract summary: We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner. We show that applying the exponential weight (EXP) learning algorithm to the stable matching game achieves logarithmic regret in a fully decentralized and uncoordinated fashion. We also introduce another decentralized and uncoordinated learning algorithm that globally converges to a stable matching with arbitrarily high probability.
• Score: 9.376820789668304
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner, where "decentralized" means that players make decisions individually without the influence of a central platform, and "uncoordinated" means that players do not need to synchronize their decisions using pre-specified rules. First, we provide a game formulation for this problem with known preferences, where the set of pure Nash equilibria (NE) coincides with the set of stable matchings, and mixed NE can be rounded to a stable matching. Then, we show that for hierarchical markets, applying the exponential weight (EXP) learning algorithm to the stable matching game achieves logarithmic regret in a fully decentralized and uncoordinated fashion. Moreover, we show that EXP converges locally and exponentially fast to a stable matching in general markets. We also introduce another decentralized and uncoordinated learning algorithm that globally converges to a stable matching with arbitrarily high probability. Finally, we provide stronger feedback conditions under which it is possible to drive the market faster toward an approximate stable matching. Our proposed game-theoretic framework bridges the discrete problem of learning stable matchings with the problem of learning NE in continuous-action games.

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