The Strategic Cores α, β, γ and δ

In a strategic cooperative game, we consider four cores α, β, γ and the one we call δ which is essentially the same to conjectural cooperative equilibria due to Currarini and Marini [2]. We show that if every player has a dominant strategy, the β-core includes the γ-core, and therefore that the four cores refine themselves in the greek alphabetical order. Two examples will be examined to see how the refinement is realized. While no strict refinement is attained at all 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.