The Component Fairness Solution for Cycle-free Graph Games
AbstractIn 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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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-114/1.
Date of creation: 12 Dec 2005
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TU-game; communication structure; Myerson value; fairness; marginal vector;
Other versions of this item:
- 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.
- Herings,P. Jean-Jacques & Laan,Gerard,van der & Talman,Dolf, 2005. "The Component Fairness Solution for Cycle- Free Graph Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-01-24 (All new papers)
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