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Sharing the cost of a network : core and core allocations

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Author Info
Koster, M.
Molina, E.
Sprumont, Y.
Tijs, S. (Tilburg University, Center for Economic Research)

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

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

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Web page: http://center.uvt.nl

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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.
  2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March. [Downloadable!] (restricted)
  5. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tijs, S.H. & Branzei, R., 2004. "Cases in cooperation and cutting the cake," Discussion Paper 108, Tilburg University, Center for Economic Research. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
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  3. Miquel, S. & Velzen, S. van & Hamers, H. & Norde, H., 2003. "Fixed tree games with repeated players," Discussion Paper 87, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Koster, M., 1999. "Weighted constrained egalitarianism in tu-games," Discussion Paper 107, Tilburg University, Center for Economic Research. [Downloadable!]
  5. Bjorndal, E. & Koster, M. & Tijs, S., 1999. "Weighted allocation rules for standard fixed tree games," Discussion Paper 79, Tilburg University, Center for Economic Research. [Downloadable!]
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