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The Component Fairness Solution for Cycle-Free Graph Games

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  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

Abstract

In this paper we study cooperative games with limited cooperation possibilities, represented by an undirected cycle-free communication graph. Players in the game can cooperate if and only if they are connected in the graph, i.e. they can communicate with one another. We introduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretation of component fairness is that deleting a link between two players yields for both resulting components the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. The component fairness solution is always in the core of the restricted game in case the game is superadditive and can be easily computed as the average of n specific marginal vectors, where n is the number of players. We also show that the component fairness solution can be generated by a specific distribution of the Harsanyi-dividends.
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Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2005. "The Component Fairness Solution for Cycle-Free Graph Games," Other publications TiSEM c4a1cae6-feed-45cd-8ee7-1, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:c4a1cae6-feed-45cd-8ee7-167d0b68253f
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    Cited by:

    1. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    2. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Other publications TiSEM e5f3ebff-9aea-4023-9525-b, Tilburg University, School of Economics and Management.

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    JEL classification:

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

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