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A note on the non-coincidence of the core and the bargaining set in many-to-one assignment markets

Author

Listed:
  • Atay, Ata
  • Núñez, Marina
  • Solymosi, Tamás

Abstract

This paper analyzes the extent to which well-known results on the relationship between the bargaining set, the core, and the kernel in one-to-one assignment games generalize to many-to-one assignment markets, and by extension, many-to-many markets. Using a minimal counterexample, we show that the bargaining set does not necessarily coincide with the core and that the kernel may not be contained within the core. We would like to highlight that the failure of the coincidence between the core and the bargaining set, as observed in the many-to-one assignment game, is quite notable. This is especially true when compared to various other highly structured games, many of which emerge from combinatorial optimization problems, such as the one underlying many-to-one assignment games.

Suggested Citation

  • Atay, Ata & Núñez, Marina & Solymosi, Tamás, 2026. "A note on the non-coincidence of the core and the bargaining set in many-to-one assignment markets," Games and Economic Behavior, Elsevier, vol. 156(C), pages 58-63.
    • Handle: RePEc:eee:gamebe:v:156:y:2026:i:c:p:58-63
    DOI: 10.1016/j.geb.2025.11.011
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    Keywords

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    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
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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