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Consistency For Proportional Solutions

Author

Listed:
  • ELENA YANOVSKAYA

    (St.Petersburg Institute for Economics and Mathematics, Russian Academy of Sciences, Tchaikovsky st. 1, 191187 St.Petersburg, Russia)

Abstract

One of the properties characterizing cooperative game solutions is consistency connecting solution vectors of a cooperative game with finite set of players and its reduced game defined by removing one or more players and by assigning them the payoffs according to some specific principle (e.g., a proposed payoff vector). Consistency of a solution means that any part (defined by a coalition of the original game) of a solution payoff vector belongs to the solution set of the corresponding reduced game. In the paper theproportional solutionsfor TU-games are defined as those depending only on the proportional excess vectors in the same manner as translation covariant solutions depend on the usual Davis–Maschler excess vectors. The general form of the reduced games defining consistent proportional solutions is given. The efficient, anonymous, proportional TU cooperative game solutions meeting the consistency property with respect to any reduced game are described.

Suggested Citation

  • Elena Yanovskaya, 2002. "Consistency For Proportional Solutions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 343-356.
  • Handle: RePEc:wsi:igtrxx:v:04:y:2002:i:03:n:s0219198902000744
    DOI: 10.1142/S0219198902000744
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    Cited by:

    1. Elena Yanovskaya, 2011. "Excess Values for Cooperative Games with Transferable Utilities and Double Consistent Allocation Methods," HSE Working papers WP BRP 10/EC/2011, National Research University Higher School of Economics.

    More about this item

    Keywords

    Games with transferable utilities; reduced game; consistency; proportional solution;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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