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The Balanced Solution for Co-operative Transferable Utility Games

Author

Listed:
  • René van den Brink

    () (Vrije Universiteit Amsterdam)

  • René Levinsky

    () (Max Planck Institute of Economics, Jena, Germany)

  • Miroslav Zeleny

    () (Charles University, Prague, 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 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.

Suggested Citation

  • René van den Brink & René Levinsky & Miroslav Zeleny, 2007. "The Balanced Solution for Co-operative Transferable Utility Games," Tinbergen Institute Discussion Papers 07-073/1, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20070073
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    References listed on IDEAS

    as
    1. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    3. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    4. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
    6. repec:spr:compst:v:51:y:2000:i:2:p:235-248 is not listed on IDEAS
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    More about this item

    Keywords

    Balanced solution; Proportionality; Reduced game consistency; Weighted Shapley value;

    JEL classification:

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

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