THE STRATEGIC CORES α, β, γ AND δ

Takashi Harada () and Mikio Nakayama ()
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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

International Game Theory Review (IGTR), 2011, vol. 13, issue 01, 45-59

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.

Keywords: Strategic cores; dominant strategy; S-Pareto Nash equilibrium; γ-core; δ-core; pure exchange game; commons game; Subject Classification: C72; Subject Classification: C71 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0219198911002836

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