A Concise Axiomatization of a Shapley-type Value for Stochastic Coalition Processes

Ulrich Faigle (1) , Michel Grabisch (2, 3)

1 Universität zu Köln = University of Cologne
2 CES - Centre d'économie de la Sorbonne
3 PSE - Paris School of Economics

The classical Shapley value is the average marginal contribution of a player, taken over all possible ways to form the grand coalition $N$ when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general coalition formation model where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is only slightly weaker than the original one but allows a much more transparent proof. Moreover, the logical independence of the axioms is exhibited.

Mots clés: Coalitional game; coalition formation process; Shapley value

Domaines: Economies et finances; Informatique et théorie des jeux [cs.GT]; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Ulrich Faigle, Michel Grabisch. A Concise Axiomatization of a Shapley-type Value for Stochastic Coalition Processes. Economic Theory Bulletin, 2013, pp.189-199. ⟨halshs-00976923⟩