Value-Free Reductions

Chaoran Sun and David Pérez-Castrillo
Authors registered in the RePEc Author Service: David Perez-Castrillo

No 1186, Working Papers from Barcelona School of Economics

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.

Keywords: shapley value; consistency; coalitional games; reduced games; axiomatization; duality (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020-06
New Economics Papers: this item is included in nep-gth and nep-mic
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Journal Article: Value-free reductions (2021)
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