IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v40y2011i1p87-110.html
   My bibliography  Save this article

Harsanyi power solutions for graph-restricted games

Author

Listed:
  • René Brink
  • Gerard Laan
  • Vitaly Pruzhansky

Abstract

This discussion paper resulted in a publication in the 'International Journal of Game Theory', 40, 87-110. 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    • Handle: RePEc:spr:jogath:v:40:y:2011:i:1:p:87-110
    DOI: 10.1007/s00182-009-0220-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-009-0220-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-009-0220-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. 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.
    5. Endre Bjørndal & Herbert Hamers & Maurice Koster, 2004. "Cost allocation in a bank ATM network," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 405-418, July.
    6. 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.
    7. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    8. 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, April.
    9. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 439-454, June.
    10. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    11. 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, February.
    12. 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 1217-1239, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    2. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    3. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
    4. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    5. Li, Daniel Li & Shan, Erfang, 2019. "The position value and the structures of graphs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 190-197.
    6. Sridhar Mandyam & Usha Sridhar, 2017. "DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence," Studies in Microeconomics, , vol. 5(2), pages 143-161, December.
    7. Kamijo, Yoshio, 2009. "A linear proportional effort allocation rule," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 341-353, November.
    8. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    9. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    10. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 47-55, September.
    11. Daniel Li Li & Erfang Shan, 2022. "Safety of links with respect to the Myerson value for communication situations," Operational Research, Springer, vol. 22(3), pages 2121-2131, July.
    12. Elena C. Gavilán & Conrado M. Manuel & René Van Den Brink, 2022. "A Family of Position Values for Directed Communication Situations," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    13. Napel, Stefan & Nohn, Andreas & Alonso-Meijide, José Maria, 2012. "Monotonicity of power in weighted voting games with restricted communication," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 247-257.
    14. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    15. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    16. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    17. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    18. Surajit Borkotokey & Loyimee Gogoi & Sudipta Sarangi, 2014. "A Survey of Player-based and Link-based Allocation Rules for Network Games," Studies in Microeconomics, , vol. 2(1), pages 5-26, June.
    19. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    20. Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Discussion Paper 2000-84, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Cooperative TU-game; Harsanyi dividend; Communication structure; Power measure; Position value; Myerson value; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:40:y:2011:i:1:p:87-110. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.