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The balanced solution for cooperative transferable utility games

Author

Listed:
  • Rene van den Brink

    (Department of Econometrics and Tinbergen Institute, Faculty of Economics and Business Administration, Free University Amsterdam)

  • Rene Levinsky

    (Max Planck Institute of Economics)

  • Miroslav Zeleny

    (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Czech Republic)

Abstract

The 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 deï¬ ne 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.

Suggested Citation

  • Rene van den Brink & Rene Levinsky & Miroslav Zeleny, 2007. "The balanced solution for cooperative transferable utility games," Jena Economics Research Papers 2007-073, Friedrich-Schiller-University Jena.
    • Handle: RePEc:jrp:jrpwrp:2007-073
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    JEL classification:

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

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