Advanced Search
MyIDEAS: Login

Harsanyi Power Solutions for Graph-restricted Games

Contents:

Author Info

  • René van den Brink

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Gerard van der Laan

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Vitaly Pruzhansky

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

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 distributions (possibly empty or consisting of a unique element) to every TU-game. Harsanyi solutions are solutions that are based on distributing dividends. In this paper we consider games with limited communication structure in which the edges or links of an undirected graph on the set of players represent binary communication links between the players such that players can cooperate if and only if they are connected. For such games we discuss Harsanyi solutions whose dividend shares are based on power measures for nodes in corresponding communication graphs. Special attention is given to the Harsanyi degree solution which equals the Shapley value on the class of complete graph games (i.e. the class of TU-games) and equals the position value on the class of cycle-free graph games. Another example is the Harsanyi power solution that is based on the equal power measure, which turns out to be the Myerson value. Various applications of our results are provided.

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/04095.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-095/1.

as in new window
Length:
Date of creation: 27 Aug 2004
Date of revision:
Handle: RePEc:dgr:uvatin:20040095

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

Related research

Keywords: cooperative TU-game; Harsanyi dividend; communication structure; power measure; position value; Myerson value; assignment games; auction games;

Other versions of this item:

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. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  2. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
  3. Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2002. "Tree-connected peer group situations and peer group games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91321, Tilburg University.
  4. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
  5. van den Nouweland, A. & Borm, P. & van Golstein, W. & Bruinderink, R.G. & Tijs, S., 1994. "A Game Theoretic Approach to Problems in Telecommunication," Papers 9407, Tilburg - Center for Economic Research.
  6. Bjorndal, E. & Hamers, H.J.M. & Koster, M.A.L., 2003. "Cost Allocation in a Bank ATM Network," Discussion Paper 2003-13, Tilburg University, Center for Economic Research.
  7. Daniel Gómez & Enrique Gonz{\'a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(2_2), pages 63-76, 02.
  8. 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.
  9. 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.
  10. 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.
  11. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-39, December.
  12. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2003. "Harsanyi Solutions in Line-graph Games," Tinbergen Institute Discussion Papers 03-076/1, Tinbergen Institute.
  13. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
  14. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  15. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
  16. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
  17. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  18. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers 01-004/1, Tinbergen Institute.
  19. Daniel Gómez & Enrique Gonz{\’a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(1), pages 63-76, 04.
  20. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
  21. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. 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.
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:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

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:20040095. 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.