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Strongly Consistent Solutions To Balanced Tu Games

Author

Listed:
  • ELENA YANOVSKAYA

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

Abstract

Consistency properties of game solutions connect between themselves the solution sets of games with different sets of players. In the paper, the strongly consistent solutions with respect to the Davis–Maschler definition of the reduced games to the class of balanced cooperative TU games with finite sets of players are considered. A cooperative game solution σ to a class${\cal G}$of a TU cooperative game is called strongly consistent if for any$\Gamma=\langle N,v\rangle \in{\cal G}$and$x\in\sigma(\Gamma)~ \sigma(\Gamma^x_S)=\sigma(\Gamma)\vert_{x_{N\setminus S}}$, where$\Gamma^x_S$is the reduced game of Γ on the player setSand with respect tox. Evidently, all consistent single-valued solutions are strongly consistent. In the paper, we characterise anonymous, covariant bounded and strongly consistent to the class${\cal G}_b\subset{\cal G}$of balanced games. The core, its relative interior and the prenucleolus are among them. However, they are not unique solutions satisfying these axioms. Thus, more axioms are necessary in order to characterise these solutions with strong consistency. One of such axioms is the definition of a solution for the class of balanced two-person games. It is sufficient for the axiomatisation of the prenucleolus without the single-valuedness axiom. If we add the closed graph property of the solution correspondence to the given axioms, then the system characterises only the core. The two axiomatisations are the main result of the paper. An example of a strongly consistent solution different from the prenucleolus, the core and its relative interior is given.

Suggested Citation

  • Elena Yanovskaya, 1999. "Strongly Consistent Solutions To Balanced Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 63-85.
  • Handle: RePEc:wsi:igtrxx:v:01:y:1999:i:01:n:s0219198999000062
    DOI: 10.1142/S0219198999000062
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    More about this item

    Keywords

    Cooperative balanced TU-game; solution; strong consistency; penucleolus; core; Primary 90D12; Secondary 90D40;
    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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