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Outside Options In Probabilistic Coalition Situations

Author

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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.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:04:n:s0219198911003076
    DOI: 10.1142/S0219198911003076
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    References listed on IDEAS

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    1. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 1-13, January.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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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    Cited by:

    1. repec:zbw:rwirep:0326 is not listed on IDEAS
    2. repec:zbw:rwirep:0456 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Julia Belau, 2013. "An outside-option-sensitive allocation rule for networks: the kappa-value," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 175-188, November.
    6. Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    7. Tobias Hiller, 2022. "Allocation of portfolio risk and outside options," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(7), pages 2845-2848, October.
    8. Belau, Julia, 2013. "Efficient Formulas and Computational Efficiency for Glove Games," Ruhr Economic Papers 456, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    9. Belau, Julia, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 326, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.

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    More about this item

    Keywords

    Coalition structure; outside option; probabilistic setting; C71;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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