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The Shapley value for shortest path games

Author

Listed:
  • Miklos Pinter

    (Department of Mathematics, Corvinus University of Budapest)

  • Anna Radvanyi

    (Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Mathematics, Corvinus University of Budapest)

Abstract

In this paper shortest path games are considered. The transportation of a good in a network has costs and benefit too. The problem is to divide the profit of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specific axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of an abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

Suggested Citation

  • Miklos Pinter & Anna Radvanyi, 2012. "The Shapley value for shortest path games," CERS-IE WORKING PAPERS 1224, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1224
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    References listed on IDEAS

    as
    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    3. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    4. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU games; Shapley value; Shortest path games; Axiomatizations of the Shapley value;
    All these keywords.

    JEL classification:

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

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