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We consider a relationship between stable outcomes and weakly setwise stable outcomes in two-sided many-to-many matching with contracts. We show that the set of stable outcomes coincides with the set of weakly setwise stable outcomes if the choice function of every agent on both sides is unitary, and the choice function of every agent on one side is substitutable, though the latter is generally larger than the former. We also show that both conditions are essential by demonstrating counterexamples each of which violates one of the conditions. Further, we discuss our results in the context of existing literature.

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Stability and Weak Setwise Stability in Many-to-Many Matching with Contracts

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  • 发表日期：

    2025年

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  • Keisuke Bando,
  • Toshiyuki Hirai

摘要

We consider a relationship between stable outcomes and weakly setwise stable outcomes in two-sided many-to-many matching with contracts. We show that the set of stable outcomes coincides with the set of weakly setwise stable outcomes if the choice function of every agent on both sides is unitary, and the choice function of every agent on one side is substitutable, though the latter is generally larger than the former. We also show that both conditions are essential by demonstrating counterexamples each of which violates one of the conditions. Further, we discuss our results in the context of existing literature.