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A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements

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  • Belau, Julia

Abstract

In an economic or social situation where agents have to group in order to achieve common goals, how can we calculate the coalitional rents of the agents arising from the coalition formation? Once we have formalized the situation via a TU-game and a network describing the economic structure, we can apply different allocation rules to assign the coalitional rents to the agents. We specifically analyze situations where parties with a specific vote distribution in a parliament have to build agreements in order to reach some required quorum. In this situation, we want to measure the (relative) distribution of power. We analyze the allocation rules called Position value (Meessen (1988) and Borm et al. (1992)) and graph-chi-value (Casajus (2009)). Applying the generalized framework (Gómez et al. (2008)), a framework where coalitions are not established yet, we fi nd that the graph-chi-value does not differ for networks referring to the same coalition while the Position value takes into account the specific role of an agent within the network, i.e. the communication path. We define and characterize a new outside option sensitive value, the Kappa-value, which takes into account both outside options and the role of an agent within the network.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:rwirep:326
    DOI: 10.4419/86788375
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    3. 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.
    4. 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.
    5. 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.
    6. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    7. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
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    More about this item

    Keywords

    Cooperative games; graph-restricted games; networks; position value; outside options; minimal winning coalitions;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H10 - Public Economics - - Structure and Scope of Government - - - General

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