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Value-free reductions

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  • Pérez-Castrillo, David
  • Sun, Chaoran

Abstract

We introduce the value-free (v-f) reductions, 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, and we characterize several v-f reductions (among which the value-free version of the reduced games proposed by Hart and Mas-Colell, 1989, and Oishi et al., 2016). Unlike reduced games, introduced to characterize values in terms of consistency, v-f reductions are not defined in reference to values. However, a v-f reduction induces a value. We characterize v-f reductions that induce the Shapley, the stand-alone, and the Banzhaf values. We connect our approach to the theory of implementation. Finally, our new approach is a valuable tool to provide new characterizations of values in terms of consistency. We present new characterizations of the Banzhaf and the stand-alone values.

Suggested Citation

  • Pérez-Castrillo, David & Sun, Chaoran, 2021. "Value-free reductions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 543-568.
    • Handle: RePEc:eee:gamebe:v:130:y:2021:i:c:p:543-568
    DOI: 10.1016/j.geb.2021.09.009
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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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