# Evolution of Coalition Structures under Uncertainty

Giuseppe De Marco and Maria Romaniello

Abstract: In Hart and Kurz (1983), stability and formation of coalition structures has been investigated in a noncooperative framework in which the strategy of each player is the coalition he wishes to join. However, given a strategy profile, the coalition structure formed is not unequivocally determined. In order to solve this problem, they proposed two rules of coalition structure formation: the $\gamma$ and the $\delta$ models. \par In this paper we look at evolutionary games arising from the $\gamma$ model for situations in which each player can choose mixed strategies and has vague expectations about the formation rule of the coalitions in which is not involved; players determine at every instant their strategies and we study how, for every player, subjective beliefs on the set of coalition structures evolve coherently to the strategic choices. Coherency is regarded as a viability constraint for the differential inclusions describing the evolutionary game. Therefore, we investigate viability properties of the constraints and characterize velocities of pairs belief/strategies which guarantee that coherency of beliefs is always satisfied. Finally, among many coherent belief revisions (evolutions), we investigate those characterized by minimal change and provide existence results.

Keywords: Coalition formation; coherent beliefs; differential inclusions; viability theory; minimal change belief revision (search for similar items in EconPapers)
JEL-codes: D71 C71 D83 C72 C73 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-evo and nep-gth
Date: 2008-03-26, Revised 2009-04-16
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