Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games
Pillage games [Jordan, 2006, "Pillage and Property", JET] have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions' power as well as to their utility. Extending von Neumann and Morgenstern's analysis of three agent games in characteristic function form to anonymous pillage games, we find: when the core is non-empty, it must take one of five forms; all such games with an empty core represent the same dominance relation. When a stable set exists, and the game also satisfies a continuity and a responsiveness axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory's flexibility.
|Date of creation:||Nov 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Edgbaston, Birmingham, B15 2TT|
Web page: http://www.economics.bham.ac.uk
More information through EDIRC
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.:
- Geoffroy de Clippel & Roberto Serrano, 2008.
"Bargaining, coalitions and externalities: A comment on Maskin,"
2008-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
- Geoffroy de Clippel & Roberto Serrano, 2008. "Bargaining, Coalitions and Externalities: a Comment on Maskin," Working Papers 2008-16, Brown University, Department of Economics.
- Stergios Skaperdas, 1996.
"Contest success functions (*),"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
- Simon MacKenzie & Manfred Kerber & Colin Rowat, 2013. "Pillage Games with Multiple Stable Sets," Discussion Papers 13-07, Department of Economics, University of Birmingham.
- Manfred Kerber & Colin Rowat, 2009.
"A Ramsey Bound on Stable Sets in Jordan Pillage Games,"
09-01r, Department of Economics, University of Birmingham.
- Manfred Kerber & Colin Rowat, 2011. "A Ramsey bound on stable sets in Jordan pillage games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 461-466, August.
- Manfred Kerber & Colin Rowat, 2009. "Stable Sets in Three Agent Pillage Games," Discussion Papers 09-07, Department of Economics, University of Birmingham.
- Alan F. Breardon & Colin Rowat, 2010. "Stable Sets in multi-good pillage games are small," Discussion Papers 10-05, Department of Economics, University of Birmingham.
- Michele Piccione & Ariel Rubinstein, 2007. "Equilibrium in the Jungle," Economic Journal, Royal Economic Society, vol. 117(522), pages 883-896, 07.
- Ray, Debraj & Vohra, Rajiv, 1997.
"Equilibrium Binding Agreements,"
Journal of Economic Theory,
Elsevier, vol. 73(1), pages 30-78, March.
- Thomas F. Hellmann & Noam Wasserman, 2011. "The First Deal: The Division of Founder Equity in New Ventures," NBER Working Papers 16922, National Bureau of Economic Research, Inc.
- Vincent Anesi, 2006. "Committees with Farsighted Voters: A New Interpretation of Stable Sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 595-610, December.
- Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590 Elsevier.
When requesting a correction, please mention this item's handle: RePEc:bir:birmec:12-11. 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: (Colin Rowat)
If references are entirely missing, you can add them using this form.