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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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  • Julia Belau

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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.

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Bibliographic Info

Paper provided by Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen in its series Ruhr Economic Papers with number 0326.

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Length: 15 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:rwi:repape:0326

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Related research

Keywords: Cooperative games; graph-restricted games; networks; position value; outside options; minimal winning coalitions;

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References

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  1. 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.
  2. 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.
  3. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  4. 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.
  5. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  6. Amandine Ghintran & Enrique Gonzalez-Arangüena & Conrado Manuel, 2010. "A probabilistic position value," Working Paper Series 1006, Óbuda University, Keleti Faculty of Business and Management.
  7. Enrique Gonz�lez-Arang�ena & Conrado Manuel & Daniel Gomez & Ren� van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
  8. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer, vol. 32(1), pages 1-13, January.
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