Problem
Research questions and friction points this paper is trying to address.
Extends matching games to one-to-many settings
Analyzes stability in strategic game-based matching
Develops polytime algorithms for bi-matrix games
Polytime Algorithms for One-to-Many Matching Games
🤖 AI Summary
This paper studies a many-to-one matching game: hospitals may match with multiple doctors, and utilities are endogenously determined by the sum of Nash equilibrium payoffs arising from a bimatrix game in which both sides employ mixed strategies. We propose, for the first time, a scalable matching game model generalizable to many-to-one settings. We design a polynomial-time solvable competitive deferred-acceptance algorithm and introduce a renegotiation mechanism to strengthen stability against unilateral deviations. Theoretically, we prove that both the algorithm and the renegotiation process run in polynomial time—even under bimatrix mixed-strategy games involving couples-type agents—ensuring computational efficiency and strategic stability. Our work extends the applicability boundary of classical matching theory and establishes a novel paradigm for resource-allocation problems modeled as strategic matching games.
📝 Abstract
Matching games is a novel matching model introduced by Garrido-Lucero and Laraki, in which agents' utilities are endogenously determined as the outcome of a strategic game they play simultaneously with the matching process. Matching games encompass most one-to-one matching market models and reinforce the classical notion of pairwise stability by analyzing their robustness to unilateral deviations within games. In this article, we extend the model to the one-to-many setting, where hospitals can be matched to multiple doctors, and their utility is given by the sum of their game outcomes. We adapt the deferred acceptance with competitions algorithm and the renegotiation process to this new framework and prove that both are polynomial whenever couples play bi-matrix games in mixed strategies.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends matching games to one-to-many
Adapts deferred acceptance algorithm
Proves polynomial complexity for bi-matrix games
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