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Outside Options In Probabilistic Coalition Situations

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  • JULIA BELAU

    ()
    (Ruhr Graduate School in Economics, Department of Economics and Social Science, University of Dortmund (TU), 44227 Dortmund, Germany)

Abstract

In this paper, we 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. We 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 as efficiency, symmetry or the null player axiom are introduced as well as new probabilistic axioms, the probabilistic influence axioms. The focus is on a generalization of the outside-option-sensitive χ-value in the new setting and an axiomatic characterization of it. The problematic of the impossibility of a direct axiomatization via deterministic pendants is discussed: As an example for a direct characterization we introduce and characterize a probabilistic version of the outside-option-insensitive pendant of the χ-value, the component restricted Shapley value. As another example for an outside-option-sensitive value without direct characterization we introduce a probabilistic version of the Owen value and show that a direct characterization is not possible; we link this to the problem of component decomposability.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 13 (2011)
Issue (Month): 04 ()
Pages: 417-442

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Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:04:p:417-442

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Related research

Keywords: Coalition structure; outside option; probabilistic setting; C71;

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References

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  1. 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.
  2. 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.
  3. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer, vol. 32(1), pages 1-13, January.
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Cited by:
  1. 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.
  2. 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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