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Sequential creation of surplus and the Shapley value

Author

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  • Álvarez-Mozos, Mikel
  • Macho-Stadler, Inés
  • Pérez-Castrillo, David

Abstract

We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present players create worth today, but the way these players organize also affects the future: their partition imposes externalities that influence the worth of coalitions formed by future players. We adapt the classic Shapley axioms and explore their implications. They are not sufficient to uniquely determine a value. We propose two solution concepts based on interpreting the Shapley value as the players' expected contributions to coalitions: the one-coalition externality value and the naive value. Our main results show that adding a single axiom to the classical Shapley axioms yields a unique value: the one-coalition externality value arises adding a principle of equal treatment of direct and indirect contributions or an axiom on necessary players, while the naive value is characterized adding equal treatment of externalities.

Suggested Citation

  • Álvarez-Mozos, Mikel & Macho-Stadler, Inés & Pérez-Castrillo, David, 2026. "Sequential creation of surplus and the Shapley value," Games and Economic Behavior, Elsevier, vol. 155(C), pages 149-166.
    • Handle: RePEc:eee:gamebe:v:155:y:2026:i:c:p:149-166
    DOI: 10.1016/j.geb.2025.09.007
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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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