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Equitable Solutions in Game Representations and the Shapley Value

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  • Pradeep Dubey

Abstract

We show that any transferable utility game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost of all facilities amongst the players in an equitable manner. The equitable solution in the representation turns out to be the Shapley value of the game, and thus serves as an alternative justification of the value. We show that this approach extends also to the case when not all coalitions can form, provided those that can constitute a semi-algebra of sets (i.e., contain the grand coalition, and are closed under complements).

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  • Pradeep Dubey, 2018. "Equitable Solutions in Game Representations and the Shapley Value," Department of Economics Working Papers 18-11, Stony Brook University, Department of Economics.
    • Handle: RePEc:nys:sunysb:18-11
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    References listed on IDEAS

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    1. Pradeep Dubey, 2018. "Intuitive Solutions in Game Representations: The Shapley Value Revisited," Cowles Foundation Discussion Papers 2123, Cowles Foundation for Research in Economics, Yale University.
    2. Pradeep Dubey, 1982. "The Shapley Value as Aircraft Landing Fees--Revisited," Management Science, INFORMS, vol. 28(8), pages 869-874, August.
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