# 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/14725/
File Function: original version

## Bibliographic Info

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

as in new window
Length:
Date of revision: 16 Apr 2009
Handle: RePEc:pra:mprapa:14725

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de

## Related research

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

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

This paper has been announced in the following NEP Reports:

## References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
1. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
2. Giuseppe De Marco & Maria Romaniello, 2006. "Dynamics of Mixed Coalitions Under Social Cohesion Constraints," Mathematical Population Studies, Taylor and Francis Journals, vol. 13(1), pages 39-62.
3. 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.
4. Aubin, Jean-Pierre & Saint-Pierre, Patrick, 2006. "Guaranteed Inertia Functions in Dynamical Games," Economics Papers from University Paris Dauphine 123456789/6881, Paris Dauphine University.
5. Andrés Perea, 2009. "A Model of Minimal Probabilistic Belief Revision," Theory and Decision, Springer, vol. 67(2), pages 163-222, August.
6. repec:ner:dauphi:urn:hdl:123456789/6881 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:14725. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.