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A weighted position value

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Author Info

  • Amandine Ghintran

    ()
    (Óbuda University)

Abstract

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in their communication links. The player who invests the most in a communication link obtains a compensation from the second one. We characterize this new allocation rule on the class of communication situations with cycle-free graphs by means of six axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. Link decomposability captures the fact that the insurance system only allows compensations between players who share a link. Weak positivity states that if the communicative strength of a link is non null, its adjacent players cannot obtain a null payoff. Finally, weak power inversion reflects the compensation mechanism.

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File URL: http://uni-obuda.hu/users/vecseya/RePEc/pkk/wpaper/1008.pdf
File Function: Manuscript, 2010
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Bibliographic Info

Paper provided by Óbuda University, Keleti Faculty of Business and Management in its series Working Paper Series with number 1008.

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Length: 24 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:pkk:wpaper:1008.rdf

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Related research

Keywords: Weighted position value; Monotonicity;

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  1. Martin Shubik, 1961. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Cowles Foundation Discussion Papers 112, Cowles Foundation for Research in Economics, Yale University.
  2. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
  3. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  4. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
  5. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer, vol. 20(2), pages 183-90.
  6. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. 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.
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