IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v07y2005i04ns021919890500065x.html
   My bibliography  Save this article

Link Monotonic Allocation Schemes

Author

Listed:
  • MARCO SLIKKER

    (BETA and Department of Technology Management, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands)

Abstract

A network is a graph where the nodes represent players and the links represent bilateral interaction between the players. A reward game assigns a value to every network on a fixed set of players. An allocation scheme specifies how to distribute the worth of every network among the players. This allocation scheme is link monotonic if extending the network does not decrease the payoff of any player. We characterize the class of reward games that have a link monotonic allocation scheme. Two allocation schemes for reward games are studied, the Myerson allocation scheme and the position allocation scheme, which are both based on allocation rules for communication situations. We introduce two notions of convexity in the setting of reward games and with these notions of convexity we characterize the classes of reward games where the Myerson allocation scheme and the position allocation scheme are link monotonic. As a by-product we find a characterization of the Myerson value and the position value on the class of reward games using potentials.

Suggested Citation

  • Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:04:n:s021919890500065x
    DOI: 10.1142/S021919890500065X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021919890500065X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021919890500065X?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. 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.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Jesus Marin Solano & Carlos Rafels Pallarola, 1996. "Convexity versus average convexity: potential, pmas, the shapley value and simple games," Working Papers in Economics 3, Universitat de Barcelona. Espai de Recerca en Economia.
    5. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    6. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
      • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    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


    Cited by:

    1. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    2. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    3. 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.
    4. 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.
    5. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    6. Nizar Allouch & Luis A.Guardiola & A. Meca, "undated". "Measuring productivity in networks: A game-theoretic approach," Studies in Economics 2302, School of Economics, University of Kent.
    7. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.
    8. Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    9. Jilei Shi & Erfang Shan, 2021. "The Banzhaf value for generalized probabilistic communication situations," Annals of Operations Research, Springer, vol. 301(1), pages 225-244, June.
    10. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    11. 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.

    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. Slikker, M., 1999. "Link Monotonic Allocation Schemes," Other publications TiSEM 42bfa59c-dba6-427e-ac48-9, Tilburg University, School of Economics and Management.
    2. 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.
    3. 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.
    4. Slikker, M., 1998. "Average Convexity in Communication Situations," Other publications TiSEM 612b0000-a66a-435a-a707-2, Tilburg University, School of Economics and Management.
    5. Slikker, M., 1998. "Average Convexity in Communication Situations," Discussion Paper 1998-12, Tilburg University, Center for Economic Research.
    6. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    7. Rodrigo J. Harrison & Roberto Munoz, 2003. "Stability and Equilibrium Selection in a Link Formation Game," Game Theory and Information 0306004, University Library of Munich, Germany.
    8. Sergio Currarini & Carmen Marchiori & Alessandro Tavoni, 2016. "Network Economics and the Environment: Insights and Perspectives," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 159-189, September.
    9. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    10. Jean-François Caulier & Ana Mauleon & Vincent Vannetelbosch, 2013. "Contractually stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 483-499, May.
    11. Roland Pongou & Roberto Serrano, 2009. "A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV/AIDS," Working Papers 2009-2, Brown University, Department of Economics.
    12. Kamijo, Yoshio, 2009. "A linear proportional effort allocation rule," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 341-353, November.
    13. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    14. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    15. Pongou, Roland & Serrano, Roberto, 2013. "Dynamic Network Formation in Two-Sided Economies," MPRA Paper 46021, University Library of Munich, Germany.
    16. Jun, Tackseung & Kim, Jeong-Yoo, 2009. "Hypergraph Formation Game," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 50(2), pages 1-16, December.
    17. Slikker, Marco & van den Nouweland, Anne, 2001. "A One-Stage Model of Link Formation and Payoff Division," Games and Economic Behavior, Elsevier, vol. 34(1), pages 153-175, January.
    18. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    20. Mutuswami, Suresh & Winter, Eyal, 2002. "Subscription Mechanisms for Network Formation," Journal of Economic Theory, Elsevier, vol. 106(2), pages 242-264, October.

    More about this item

    Keywords

    Network; reward game; monotonic allocation scheme; Journal of Economic Literature Classification Numbers: C71;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:07:y:2005:i:04:n:s021919890500065x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.