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Values for Cooperative Games over Graphs and Games With Inadmissible Coalitions

Author

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  • Ziv Hellman

    (Bar-Ilan University)

  • Ron Peretz

Abstract

We suppose that players in a cooperative game are located within a graph structure, such as a social network or supply route, that limits coalition formation to coalitions along connected subsets within the graph. This in turn leads to a more general study of coalitional games in which there are arbitrary limitations on the collections of coalitions that may be formed. Within this context we define a generalisation of the Shapley value that is studied from an axiomatic perspective. The resulting ‘graph value’ (and ‘S-value’ in the general case) is endogenously asymmetric, with the automorphism group of the graph playing a crucial role in determining the relative values of players.

Suggested Citation

  • Ziv Hellman & Ron Peretz, 2015. "Values for Cooperative Games over Graphs and Games With Inadmissible Coalitions," Working Papers 2015-04, Bar-Ilan University, Department of Economics.
    • Handle: RePEc:biu:wpaper:2015-04
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    References listed on IDEAS

    as
    1. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    2. Nimrod Megiddo, 1978. "Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 189-196, August.
    3. Françoise Forges & Roberto Serrano, 2013. "Cooperative Games With Incomplete Information: Some Open Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-17.
    4. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    5. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.
    6. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Edelman, Paul H., 1997. "A note on voting," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 37-50, August.
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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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