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The component fairness solution for cycle-free graph games

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Author Info
Herings, P. Jean-Jacques
Laan, Gerard van der
Talman, Dolf (Tilburg University, Center for Economic Research)

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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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 127.

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Date of creation: 2005
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Handle: RePEc:dgr:kubcen:2005127

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Web page: http://center.uvt.nl

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Related research
Keywords: TU-games; communication structure; Myerson value; fairness; marginal vector; 90B18; 91A12; 91A43;

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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References listed on IDEAS
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  1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November. [Downloadable!] (restricted)
  2. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
  3. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation, Yale University. [Downloadable!]
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  4. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January. [Downloadable!] (restricted)
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  5. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, vol. 20(4), pages 419-27.
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  6. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  7. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  8. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute. [Downloadable!]
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Cited by:
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  1. Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "Balanced per capita contributions and levels structure of cooperation," MPRA Paper 8208, University Library of Munich, Germany. [Downloadable!]
  2. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research. [Downloadable!]
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