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In the growing literature on game theory, continuous attention has been drawn to a theorem by Novshek (1985) on the existence of equilibrium in Cournot oligopoly games. This theorem is of substantial importance because it gives an equilibrium in a most general setting of a Cournot model without assuming convexity of firms' cost functions. Furthermore, it weakens the assumption of concave inverse demand. However, the proof of this theorem provided by Novshek (1985) is not very well clarified. In addition to this, the proof is not complete in the sense that it only considers situations where firms' best response correspondences have continuous branches. Realizing this incompleteness, Kukushkin (1994) gave a rigorous proof beginning with a discrete version of the Cournot model. Kukushkin's proof is a complete and satisfactory one, but unfortunately there has not been an alternative proof given from a different perspective than his in the existing literature. This became the main motivation for this thesis. In this thesis, I provide a clarification of Novshek's original proof, discuss the refinement by Kukushkin (1994), and give an alternative proof of Novshek's theorem.
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