Abstract
We study what coalitions form and how the members of each coalition split the coalition value in coalitional games in which only individual deviations are allowed. In this context we employ three stability notions: individual, contractual, and compensational stability. These notions differ in terms of the underlying contractual assumptions. We characterize the coalitional games in which individually stable outcomes exist by means of the top-partition property. Furthermore, we show that any coalition structure of maximum social worth is both contractually and compensationally stable.
Applying the general framework to an example of mutual insurance in production, we find that in each type of contractual setting there are stable individually rational pooling outcomes, while, on the contrary, individually rational separating outcomes are not stable in general. In addition, we study monotonic simple proper games and establish that any outcome containing a winning coalition is both contractually and compensationally stable. We show that an individually stable outcome containing a winning coalition always exists, and characterize all such outcomes.
Similar content being viewed by others
References
Aumann RJ, Dreze JH (1974) Cooperative games with coalition structure. Int J Game Theory 3:217–237
Banerjee S, Konishi H, Sonmez T (2001) Core in a simple coalition formation game. Soc Choice Welf 18:135–153
Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59(3):595–609
Bloch F, Jackson MO (2006) Definitions of equilibrium in network formation games. Int J Game Theory 34(3):305–318
Bloch F, Jackson MO (2007) The formation of networks with transfers among players. J Econ Theory 133(1):83–110
Boehm V (1974) The core of economy with production. Rev Econ Stud 41:429–436
Boyd J, Prescott E, Smith B (1988) Organizations in economic analysis. Can J Econ 21:477–491
Dreze JH, Greenberg J (1980) Hedonic coalitions: optimality and stability. Econometrica 48(4):987–1003
Lazarova E, Borm P, Montero M, Reijnierse H (2009) A bargaining set for monotonic simple games based on external and internal stability. TOP. doi:10.1007/s11750-009-0079-2. Available online: http://www.springerlink.com/content/10n6228301k43m24/
Morelli M, Montero M (2003) The demand bargaining set: general characterization and application to weighted majority games. Games Econ Behav 42(1):137–155
Peleg B (1967) Existence theorem for the bargaining set \(\mathcal{M}^{(i)}_{l}\). In: Shubik M (ed) Essays in mathematical economics in honour of Oskar Morgenstern. Princeton University Press, Princeton, pp 53–56
Rothschild M, Stiglitz J (1976) Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Q J Econ 90(4):629–649
Scotchmer S, Jehiel P (2001) Constitutional rules of exclusion in jurisdiction formation. Rev Econ Stud 68:393–411
Shapley L (1962) Simple games: an outline of the descriptive theory. Behav Sci 7:59–66
Sperling L, Osborn T, Cooper D (eds) (2004) Towards effective and sustainable seed relief activities. Report on the workshop on effective and sustainable seed relief activities, Rome, 26–28 May, 2003
Zhou L (1994) A new bargaining set of an n-person game and endogenous coalition formation. Games Econ Behav 6:512–526
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lazarova, E., Borm, P. & van Velzen, B. Coalitional games and contracts based on individual deviations. TOP 19, 507–520 (2011). https://doi.org/10.1007/s11750-010-0149-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-010-0149-5