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Distributing Dividends in Games with Ordered Players

Author

Listed:
  • René van den Brink

    (Vrije Universiteit Amsterdam)

  • Gerard van der Laan

    (Vrije Universiteit Amsterdam)

  • Valeri Vasil'ev

    (Sobolev Institute of Mathematics, Novosibirsk)

Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff vectors to every TU-game. Some solutions that are based on distributing dividends are the Shapley value (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions) and the Selectope or Harsanyi set (being the set-valued solution that contains all possible distributions of the dividends among the players in the corresponding coalitions). In this paper we assume the players to be hierarchically ordered. We modify the concept of Harsanyi set to this context by taking into account this hierarchical order when distributing the dividends of the game. We show that the resulting new solution concept for games with ordered players, called the Restricted Harsanyi set, is fully characterized by a collection of seven logically independent properties. We also discuss an alternative modification of the Harsanyi set and a solution concept resulting from adapting the concept of Selectope to games with ordered players. Some applications show the usefulness of the Restricted Harsanyi set.

Suggested Citation

  • René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers 06-114/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20060114
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    References listed on IDEAS

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    More about this item

    Keywords

    TU-game; Harsanyi dividends; Shapley value; Harsanyi set; Selectope; digraph;
    All these keywords.

    JEL classification:

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

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