# Evolution of Coalition Structures under Uncertainty

## Author Info

• De Marco, Giuseppe
• Romaniello, Maria

## 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.

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File URL: http://mpra.ub.uni-muenchen.de/14725/5/MPRA_paper_14725.pdf
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## Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14725.

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 Length: Date of creation: 26 Mar 2008 Date of revision: 16 Apr 2009 Handle: RePEc:pra:mprapa:14725 Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, GermanyPhone: +49-(0)89-2180-2219Fax: +49-(0)89-2180-3900Web page: http://mpra.ub.uni-muenchen.deMore information through EDIRC

## References

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1. Aubin, Jean-Pierre & Saint-Pierre, Patrick, 2006. "Guaranteed Inertia Functions in Dynamical Games," Economics Papers from University Paris Dauphine 123456789/6881, Paris Dauphine University.
2. Jean-Pierre Aubin, 2003. "Regulation of the evolution of the architecture of a network by tensors operating on coalitions of actors," Journal of Evolutionary Economics, Springer, vol. 13(2), pages 95-124, 04.
3. Giuseppe De Marco & Maria Romaniello, 2006. "Dynamics of Mixed Coalitions Under Social Cohesion Constraints," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 39-62.
4. Andrés Perea, 2009. "A Model of Minimal Probabilistic Belief Revision," Theory and Decision, Springer, vol. 67(2), pages 163-222, August.
5. Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
6. Jean-Pierre Aubin & Patrick Saint-Pierre, 2006. "Guaranteed Inertia Functions In Dynamical Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 185-218.
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