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The Strategic Cores Α, Β, Γ And Δ

Author

Listed:
  • TAKASHI HARADA

    (Graduate School of Economics, Keio University, Minato-ku, Tokyo 108-8345, Japan)

  • MIKIO NAKAYAMA

    (Department of Economics, Keio University, 2-15-45, Mita, Minato-ku, Tokyo 108-8345, Japan)

Abstract

In a strategic coalitional game, we consider the relations among four cores α, β, γ, and the one we call δ which is obtained by slightly weakening theconjectural cooperative equilibriadue to Currarini and Marini. We show that the α-core and the γ-core are refined by the δ-core; and, moreover that if every player has a dominant strategy, the β-core is refined by the γ-core, so that the four cores refine themselves in the greek alphabetical order. Two economic games will be considered to show that the refinement of the α-core can vary from the weakest to the strongest. While the four cores are equal in the pure exchange game, a radical reduction of the α-core is obtained in the commons game, a simple version of the Cournot game, bringing about a single strategy profile as the δ-core.

Suggested Citation

  • Takashi Harada & Mikio Nakayama, 2011. "The Strategic Cores Α, Β, Γ And Δ," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 45-59.
    • Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:01:n:s0219198911002836
    DOI: 10.1142/S0219198911002836
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    References listed on IDEAS

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    1. Carlo Carraro & Vito Fragnelli (ed.), 2004. "Game Practice and the Environment," Books, Edward Elgar Publishing, number 3344.
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    More about this item

    Keywords

    Strategic cores; dominant strategy; S-Pareto Nash equilibrium; γ-core; δ-core; pure exchange game; commons game; Subject Classification: C72; Subject Classification: C71;
    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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