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Sequential Creation of Surplus and the Shapley Value

Author

Listed:
  • Mikel à lvarez-Mozos

    (Universitat de Barcelona and BEAT)

  • Inés MachoStadler

    (Universitat Autónoma de Barcelona and BSE)

  • David PérezCastrillo

    (Universitat Autónoma de Barcelona and BSE)

Abstract

We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today’s partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players’ expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value.

Suggested Citation

  • Mikel à lvarez-Mozos & Inés MachoStadler & David PérezCastrillo, 2024. "Sequential Creation of Surplus and the Shapley Value," UB School of Economics Working Papers 2024/466, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:466web
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    References listed on IDEAS

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    1. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    2. McQuillin, Ben, 2009. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," Journal of Economic Theory, Elsevier, vol. 144(2), pages 696-721, March.
    3. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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