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Value-Free Reductions

Author

Listed:
  • David Pérez-Castrillo
  • Chaoran Sun
Abstract
We introduce the value-free (v-f ) reductions, which are operators that map a coalitional game played by a set of players to another "similar" game played by a subset of those players. We propose properties that v-f reductions may satisfy, we provide a theory of duality for them, and we characterize several v-f reductions (among which the value-free version of the reduced games propose by Hart and Mas-Colell, 1989, and Oishi et al., 2016). Unlike reduced games, which were introduced to characterize values in terms of consistency properties, v-f reductions are not defined in reference to values. However, a "path-independent" v-f reduction induces a value. We characterize v-f reductions that induce the Shapley value, the stand-alone value, and the Banzhaf value. Moreover, we can connect our approach to the literature on consistency because any value induced by a path-independent v-f reduction is consistent with that reduction.

Suggested Citation

  • David Pérez-Castrillo & Chaoran Sun, 2020. "Value-Free Reductions," Working Papers 1186, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1186
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    References listed on IDEAS

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    Cited by:

    1. Sun, Chaoran, 2022. "Bidding against a Buyout: Implementing the Shapley value and the equal surplus value," Journal of Mathematical Economics, Elsevier, vol. 101(C).

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    More about this item

    Keywords

    coalitional games; reduced games; axiomatization; consistency; shapley value; duality;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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