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

The classical Shapley value is the averagemarginal 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 muchmore transparent proof.More-over, the logical independence of the axioms is exhibited