A coalition formation value for games in partition function form

Michel Grabisch (1) , Yukihiko Funaki (2)

1 CES - Centre d'économie de la Sorbonne
2 School of political science and economics, Waseda University

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.

Mots clés: game theory; coalition formation; games in partition function form; Shapley value

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

Michel Grabisch, Yukihiko Funaki. A coalition formation value for games in partition function form. European Journal of Operational Research, 2012, pp.175-185. ⟨halshs-00690696⟩