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 the evolutionary games arising from the $\gamma$ and $\delta$ models in which players determine at every instant their strategies and, in particular, we study how the coalition structure evolve according to the strategic choices. For this purpose we consider mixed strategies and, firstly, we notice that natural generalizations of the $\gamma$ and $\delta$ models to this case lead to multiplicity of beliefs (on the set of coalition structures) coherent with the probability assignments given by the strategy profile. Coherency is regarded as a viability constraint for the differential inclusions describing the evolutionary games. 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.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
10923.
Find related papers by JEL classification: D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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