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Self-consistency for multi-valued solutions and reasonable outcomes

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  • Calleja, Pedro
  • Llerena, Francesc
  • Sudhölter, Peter

Abstract

We explore the compatibility of uniform self-consistency and ordinary self-consistency, two extensions for handling multi-valued solutions within the consistency principle introduced by Hart and Mas-Colell (1989), with basic properties, such as reasonableness, which establishes bounds for payoffs based on the marginality principle. Our analysis focuses on convex games and balanced games through the study of almost positive games, a subset of convex games that plays a crucial role in the vector lattice structure of games. Further, we provide new axiomatic foundations of the core incorporating these consistency properties.

Suggested Citation

  • Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2025. "Self-consistency for multi-valued solutions and reasonable outcomes," Journal of Mathematical Economics, Elsevier, vol. 120(C).
    • Handle: RePEc:eee:mateco:v:120:y:2025:i:c:s0304406825000886
    DOI: 10.1016/j.jmateco.2025.103171
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    References listed on IDEAS

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    8. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2020. "Sharing the Revenues from Broadcasting Sport Events," Management Science, INFORMS, vol. 66(6), pages 2417-2431, June.
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    JEL classification:

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

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