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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.

A concise axiomatization of a Shapley-type value for stochastic coalition processes