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The Strategic Cores Α, Β, Γ And Δ

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  • 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)

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    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 the conjectural cooperative equilibria due 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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 13 (2011)
    Issue (Month): 01 ()
    Pages: 45-59

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    Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:01:p:45-59

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    Related research

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

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