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The Harsanyi Set for Cooperative TU-Games

Author

Listed:
  • Valeri Vasil'ev

    (Sobolev Institute of Mathematics, Russia)

  • Gerard van der Laan

    (Vrije Universiteit Amsterdam)

Abstract

This discussion paper resulted in a publication in 'Siberian Advances in Mathematics', 2002, 12, 97-125. A cooperative game with transferable utilities, or simply aTU-game, describes a situation in which players can obtain certainpayoffs by cooperation. A solution mapping for these games is amapping which assigns to every game a set of payoff distributionsover the players in the game. Well-known solution mappings are the Coreand the Weber set. In this paper we consider the mapping assigning toevery game the Harsanyi set being the set of payoff vectors obtained byall possible distributions of the Harsanyi dividends of a coalitionamongst its members. We discuss the structure and properties of thismapping and show how the Harsanyi set is related to the Core and Weberset. We also characterize the Harsanyi mapping as the unique mappingsatisfying a set of six axioms. Finally we discuss some properties of the Harsanyi Imputation set, being the individally rational subset of the Harsanyi set.

Suggested Citation

  • Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers 01-004/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010004
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    Cited by:

    1. David Lowing & Makoto Yokoo, 2023. "Sharing values for multi-choice games: an axiomatic approach," Working Papers hal-04018735, HAL.

    More about this item

    Keywords

    Core; Harsanyi Set; Weber Set; Shapley Value; Selectope;
    All these keywords.

    JEL classification:

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

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