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Core Representations of the Standard Fixed Tree Game

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  • Koster, M.A.L.
  • Molina, E.
  • Sprumont, Y.
  • Tijs, S.H.

    (Tilburg University, Center for Economic Research)

Abstract

This paper discusses the core of the game corresponding to the standard fixed tree problem. We introduce the concept of a weighted constrained egalitarian solution. The core of the standard fixed tree game equals the set of all weighted constrained egalitarian solutions. The notion of home-down allocation is developed to create further insight in the local behavior of the weighted constrained egalitarian allocation. A similar and dual approach by the notion of down-home allocations gives us the class of weighted Shapley values. The constrained egalitarian solution is characterized in terms of a cost sharing mechanism.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1998-21.

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Date of creation: 1998
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Handle: RePEc:dgr:kubcen:199821

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Related research

Keywords: Cooperative game theory; tree games; core; weighted constrained egalitarian solution;

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References

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  1. Granot, D, et al, 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer, vol. 25(2), pages 219-44.
  2. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
  3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  4. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  5. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
  6. Dragan, I. & Potters, J.A.M. & Tijs, S.H., 1989. "Superadditivity for solutions of coalitional games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154238, Tilburg University.
  7. Pradeep Dubey, 1982. "The Shapley Value as Aircraft Landing Fees--Revisited," Management Science, INFORMS, vol. 28(8), pages 869-874, August.
  8. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Jos Potters & Peter Sudhölter, 1995. "Airport Problems and Consistent Solution Rules," Working Papers 246, Bielefeld University, Center for Mathematical Economics.
  10. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
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Citations

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Cited by:
  1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
  2. Koster, M.A.L., 1999. "Weighted Constrained Egalitarianism in TU-Games," Discussion Paper 1999-107, Tilburg University, Center for Economic Research.

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