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Values for cooperative games over graphs and games with inadmissible coalitions

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  • Hellman, Ziv
  • Peretz, Ron

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

  • Hellman, Ziv & Peretz, Ron, 2018. "Values for cooperative games over graphs and games with inadmissible coalitions," Games and Economic Behavior, Elsevier, vol. 108(C), pages 22-36.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:22-36
    DOI: 10.1016/j.geb.2016.12.007
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    More about this item

    Keywords

    Shapley value; Network games;

    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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