De Marco, Giuseppe and Romaniello, Maria (2008): Evolution of Coalition Structures under Uncertainty.

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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.
Item Type:  MPRA Paper 

Original Title:  Evolution of Coalition Structures under Uncertainty 
Language:  English 
Keywords:  Coalition formation; coherent beliefs; differential inclusions; viability theory; minimal change belief revision 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice; Clubs; Committees; Associations C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search; Learning; Information and Knowledge; Communication; Belief C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games 
Item ID:  14725 
Depositing User:  G. De Marco 
Date Deposited:  21. Apr 2009 00:10 
Last Modified:  15. Feb 2013 16:27 
References:  1] Aubin J.P. (1974): Coeur et Valeur des Jeux Flous ¶a Paiements Lat¶eraux, C.R. Acad. Sci. Paris, 279 A, 891894. [2] Aubin J.P. (1981): Locally Lipchitz Cooperative Games, Journal of Mathematical Economics, 8, 241262. [3] Aubin J.P. (1991): Viability Theory, Birkhauser. [4] Aubin J.P. (1997): Dynamic Economic Theory: A Viability Approach, Springer. [5] Aubin J.P. (2002): Dynamic Core of Fuzzy Cooperative Games, Annals of Dynamic Games, 7. [6] Aubin J.P. (2003): Regulation of the Evolution of the Architecture of a Network by Connectionist Tensors Operating on Coalitions of Actors, Journal of Evolutionary Economics, 13, 95124. [7] Aubin J.P. and H. Frankowska (1990): Set Valued Analysis, Birkhauser. [8] Aubin J.P. and P. SaintPierre (2006): Guaranteed Inertia Functions in Dynamical Games, International Game Theory Review, 8(2),185218 [9] Clarke F.H., Ledyaev Y.S., Stern R.J and P.R. Wolenski (1998): Nonsmooth Analysis and Control Theory, Springer. [10] de Finetti B. (1931): Sul Signi¯cato Soggettivo della Probabilitµa, Fundamenta Mathematicae, T. XVIII, 298329. [11] De Marco G. and M. Romaniello (2006): Dynamics of Mixed Coalitions under Social Cohesion Constraints, Mathematical Population Studies, 13(1), 3962. [12] Filar J.A. and L.A. Petrosjan (2000): Dynamic Cooperative Games, International Game Theory Review, 2, 4765. [13] Greenberg J. (2002): Coalition Structures. Chapter 37 in Handbook of Game Theory with Economic Applications, Volume 2, Elsevier Science Publishers (NorthHolland), Amsterdam. [14] Hart S. and M. Kurz (1983): Endogenous Coalition Formation, Econometrica, 51(4), 10471064. [15] Konishi H. and D.Ray(2003): Coalition Formation as a Dynamic Process, Journal of Economic Theory, 110, 141 [16] Myerson R. (1978): Graphs and cooperation in games, Mathematics of Operations Research, 2, 225229. [17] Owen G. (1977): Values of garnes with a priori unions, in Essays in Mathematical Economics and Garne Theory, R. Hein and O. Moesehlin (ed.),New York: SpringerVerlag, pp. 7688. [18] Perea A. (2007): A Model of Minimal Probabilistic Belief Revision, Theory and Decision, to appear, on line version available. [19] Rockafellar R.T. and R.JB. Wets (1998): Variational Analysis, Springer. [20] Schulte, O. (2002): Minimal Belief Change, ParetoOptimality and Logical Consequences, Eco nomic Theory, 19, 105144. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/14725 