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Equitable Solutions in Game Representations: An Extension of the Shapley Value

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  • Pradeep Dubey

Abstract

We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the Shapley value of the game, and thus provides as an alternative justication of the value. Game representations also open the door for extending the Shapley value to situations where not all coalitions can form, provided those that can constitute a quasi-algebra; or, more generally, a hierarchy; or, still more generally, have full span.

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  • Pradeep Dubey, 2024. "Equitable Solutions in Game Representations: An Extension of the Shapley Value," Department of Economics Working Papers 24-01, Stony Brook University, Department of Economics.
    • Handle: RePEc:nys:sunysb:24-01
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    References listed on IDEAS

    as
    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. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. 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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