The Component Fairness Solution for Cycle- Free Graph Games
AbstractIn this paper we study cooperative games with limited cooperation possibilities, representedby an undirected cycle-free communication graph. Players in the game can cooperate if andonly if they are connected in the graph, i.e. they can communicate with one another. Weintroduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretationof component fairness is that deleting a link between two players yields for both resultingcomponents 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. Thecomponent fairness solution is always in the core of the restricted game in case the gameis 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 canbe generated by a specific distribution of the Harsanyi-dividends.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 056.
Date of creation: 2005
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operations research and management science;
Other versions of this item:
- P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2005. "The Component Fairness Solution for Cycle-free Graph Games," Tinbergen Institute Discussion Papers 05-114/1, Tinbergen Institute.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2005. "The Component Fairness Solution for Cycle-Free Graph Games," Discussion Paper 2005-127, Tilburg University, Center for Economic Research.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-01-01 (All new papers)
- NEP-GTH-2006-01-01 (Game Theory)
- NEP-KNM-2006-01-01 (Knowledge Management & Knowledge Economy)
- NEP-SOC-2006-01-01 (Social Norms & Social Capital)
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