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Link Monotonic Allocation Schemes

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  • Slikker, M.

    (Tilburg University, Center For Economic Research)

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.
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Suggested Citation

  • Slikker, M., 1999. "Link Monotonic Allocation Schemes," Discussion Paper 1999-06, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:42bfa59c-dba6-427e-ac48-9914d9b4780c
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    References listed on IDEAS

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    1. 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.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
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    4. 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.
    5. 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.
    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.
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    Citations

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    Cited by:

    1. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    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. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    4. 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.
    5. Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    6. 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.
    7. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    8. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.
    9. 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.
    10. 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.
    11. 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.

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    More about this item

    Keywords

    network; reward game; monotonic allocation scheme;
    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

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