A \(\beta\)-core existence result and its application to oligopoly markets. (English) Zbl 0926.91031
Summary: This paper establishes a \(\beta\)-core existence result in a large class of normal form TU (transferable utility) games. In the oligopoly markets of a homogeneous good, the TU \(\beta\)-core is always equal to the TU \(\alpha\)-core, and they are nonempty if all profit functions are continuous and concave. In a general game, the TU \(\beta\)-core is nonempty if (a) all strategy sets are compact and convex, (b) all payoff functions are continuous and concave, and (c) the game satisfies the strong separability.
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