Outside Options in Probabilistic Coalition Situations
AbstractIn this paper, I introduce an extension of (TU) games with a coalition structure. Taking a situation where all coalitions are already established is not reasonable in order to forecast the reality; there is not only one possible coalition, there are several. I consider situations where coalitions are not established yet and take into account the likelihood of each possible coalition. This leads to a generalized, probabilistic setting for coalition structures. Probabilistic versions of known axioms are introduced as well as new probabilistic axioms. Generalizations of both the outside-option-sensitive chi-value (Casajus, Soc Choice Welf 32, 1-13, 2009) and its outside-option-insensitive pendant, the component restricted Shapley value (Aumann and Drèze, Int. J. Game Theory 3, 217-237, 1974), are defined and axiomatic characterizations are given.
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Bibliographic InfoPaper provided by Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen in its series Ruhr Economic Papers with number 0236.
Length: 28 pages
Date of creation: Jan 2011
Date of revision:
Other versions of this item:
- Julia Belau, 2011. "Outside Options In Probabilistic Coalition Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 417-442.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-18 (All new papers)
- NEP-CDM-2011-06-18 (Collective Decision-Making)
- NEP-GTH-2011-06-18 (Game Theory)
- NEP-NET-2011-06-18 (Network Economics)
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.:
- Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
- André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer, vol. 32(1), pages 1-13, January.
- Shapley, Lloyd S & Shubik, Martin, 1969. "Pure Competition, Coalitional Power, and Fair Division," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 337-62, October.
- Julia Belau, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 0326, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
- Julia Belau, 2013. "Effi cient Formulas and Computational Efficiency for Glove Games," Ruhr Economic Papers 0456, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
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