Advanced Search
MyIDEAS: Login

Distributing Dividends in Games with Ordered Players

Contents:

Author Info

  • René van den Brink

    ()
    (Vrije Universiteit Amsterdam)

  • Gerard van der Laan

    ()
    (Vrije Universiteit Amsterdam)

  • Valeri Vasil'ev

    ()
    (Sobolev Institute of Mathematics, Novosibirsk)

Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff vectors to every TU-game. Some solutions that are based on distributing dividends are the Shapley value (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions) and the Selectope or Harsanyi set (being the set-valued solution that contains all possible distributions of the dividends among the players in the corresponding coalitions). In this paper we assume the players to be hierarchically ordered. We modify the concept of Harsanyi set to this context by taking into account this hierarchical order when distributing the dividends of the game. We show that the resulting new solution concept for games with ordered players, called the Restricted Harsanyi set, is fully characterized by a collection of seven logically independent properties. We also discuss an alternative modification of the Harsanyi set and a solution concept resulting from adapting the concept of Selectope to games with ordered players. Some applications show the usefulness of the Restricted Harsanyi set.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://papers.tinbergen.nl/06114.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-114/1.

as in new window
Length:
Date of creation: 02 Jan 2007
Date of revision:
Handle: RePEc:dgr:uvatin:20060114

Contact details of provider:
Web page: http://www.tinbergen.nl

Related research

Keywords: TU-game; Harsanyi dividends; Shapley value; Harsanyi set; Selectope; digraph;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer, vol. 18(2), pages 227-40.
  2. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers 01-004/1, Tinbergen Institute.
  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.
  4. Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991. "Games with permission structures: The conjunctive approach," Discussion Paper 1991-14, Tilburg University, Center for Economic Research.
  5. 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.
  6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  7. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1978. "Barriers to trade and disadvantageous middlemen: Nonmonotonicity of the core," Journal of Economic Theory, Elsevier, vol. 19(1), pages 200-209, October.
  8. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2004. "On the Extreme Points of Two Polytopes associated with a Digraph and Applications to Cooperative Games," Tinbergen Institute Discussion Papers 04-069/1, Tinbergen Institute.
  9. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
  10. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  11. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
  12. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
  13. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2004. "The Socially Stable Core in Structured Transferable Utility Games," Tinbergen Institute Discussion Papers 04-043/1, Tinbergen Institute.
  2. Ren� van den Brink & Gerard van der Laan & Valeri Vasil'ev, 0000. "The Restricted Core for Totally Positive Games with Ordered Players," Tinbergen Institute Discussion Papers 09-038/1, Tinbergen Institute.
  3. van den Brink, René & van der Laan, Gerard & Vasil'ev, Valeri, 2008. "Extreme points of two digraph polytopes: Description and applications in economics and game theory," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1114-1125, December.
  4. repec:hal:cesptp:halshs-00583868 is not listed on IDEAS

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:dgr:uvatin:20060114. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.