A coalition formation value for games in partition function form

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give also two axiomatizations of our coalition formation value.

► a value suited to coalition formation for games with externalities.
► The value is an average of marginal contribution of players in scenarios.
► The classical Shapley value and the de Clippel–Serrano value can be recovered.