A coalition formation value for games in partition function form

• Published in: European journal of operational research Vol. 221; no. 1; pp. 175 - 185
• Main Authors: Grabisch, Michel, Funaki, Yukihiko
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.08.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied sciences; Associations; Coalition formation; Coalitions; Computer Science; Computer Science and Game Theory; Discrete Mathematics; Economic models; Economics; Economics and Finance; Exact sciences and technology; Externalities; Externality; Game theory; Games; Games in partition function form; Humanities and Social Sciences; Mathematical models; Operational research; Operational research and scientific management; Operational research. Management science; Operations Research; Partitions; Players; Shapley value; Studies; Coalition formation; Games in partition function form; Shapley value; Game theory; Partition; Script; Game value; Externality; Surplus; Economy; Partition function; Coalition; Cooperative game; games in partition function form; coalition formation; game theory
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.02.036

► 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. 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.