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Stability properties of the core in a generalized assignment problem

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  • Bando, Keisuke
  • Kawasaki, Ryo

Abstract

We show that the core of a generalized assignment problem satisfies two types of stability properties. First, the core is the unique stable set defined using the weak domination relation when outcomes are restricted to individually rational and pairwise feasible ones. Second, the core is the unique stable set with respect to a sequential domination relation that is defined by a sequence of weak domination relations that satisfy outsider independence. An equivalent way of stating this result is that the core satisfies the property commonly stated as the existence of a path to stability. These results add to the importance of the core in an assignment problem where agents' preferences may not be quasilinear.

Suggested Citation

  • Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    • Handle: RePEc:eee:gamebe:v:130:y:2021:i:c:p:211-223
    DOI: 10.1016/j.geb.2021.08.007
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    More about this item

    Keywords

    Generalized assignment problem; Core; Stable set; Path to stability;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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