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Coalition-weighted Shapley values

Author

Listed:
  • Estela Sánchez-Rodríguez

    (Universidade de Vigo)

  • Miguel Ángel Mirás Calvo

    (Universidade de Vigo)

  • Carmen Quinteiro Sandomingo

    (Universidade de Vigo)

  • Iago Núñez Lugilde

    (Universidade de Vigo)

Abstract

We introduce a new class of values for coalitional games: the coalition-weighted Shapley values. Weights can be assigned to coalitions, not just to players, and zero-weights are admissible. The Shapley value belongs to this class. Coalition-weighted Shapley values recommend for each game the allocation defined by the Shapley value of a weighted game obtained as a linear convex combination of the associated marginal games. Coalition-weighted Shapley values are random order values and Harsanyi values. Positively weighted Shapley values and weighted Shapley values can be seen as the limit of a sequence of iterated coalition-weighted Shapley values. We provide axiomatic characterizations of coalition-weighted Shapley values through properties that do not involve the weights. Finally, we discuss how to extend our model to include exogenous coalition structures as in the hierarchical and Owen values.

Suggested Citation

  • Estela Sánchez-Rodríguez & Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Iago Núñez Lugilde, 2024. "Coalition-weighted Shapley values," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 547-577, June.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:2:d:10.1007_s00182-023-00877-w
    DOI: 10.1007/s00182-023-00877-w
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    References listed on IDEAS

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