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# Evolution of Coalition Structures under Uncertainty

## Author

Listed:
• 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.

## Suggested Citation

• De Marco, Giuseppe & Romaniello, Maria, 2008. "Evolution of Coalition Structures under Uncertainty," MPRA Paper 14725, University Library of Munich, Germany, revised 16 Apr 2009.
• Handle: RePEc:pra:mprapa:14725
as

File URL: https://mpra.ub.uni-muenchen.de/14725/5/MPRA_paper_14725.pdf
File Function: original version

## References listed on IDEAS

as
1. 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.
2. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
3. repec:dau:papers:123456789/6881 is not listed on IDEAS
4. Andrés Perea, 2009. "A Model of Minimal Probabilistic Belief Revision," Theory and Decision, Springer, vol. 67(2), pages 163-222, August.
5. 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, April.
Full references (including those not matched with items on IDEAS)

### Keywords

Coalition formation; coherent beliefs; differential inclusions; viability theory; minimal change belief revision;

### 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; Information and Knowledge; Communication; Belief; Unawareness
• 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

### NEP fields

This paper has been announced in the following NEP Reports:

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