Outside Options in Probabilistic Coalition Situations
In 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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- 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.
- André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer, vol. 32(1), pages 1-13, January.
- 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.
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