The Balanced Solution for Co-operative Transferable Utility Games
AbstractThe Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we define the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 07-073/1.
Date of creation: 12 Oct 2007
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Balanced solution; Proportionality; Reduced game consistency; Weighted Shapley value;
Other versions of this item:
- Rene van den Brink & Rene Levinsky & Miroslav Zeleny, 2007. "The balanced solution for cooperative transferable utility games," Jena Economic Research Papers 2007-073, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-23 (All new papers)
- NEP-GTH-2008-02-23 (Game Theory)
- NEP-UPT-2008-02-23 (Utility Models & Prospect Theory)
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