On equivalence between Cournot competition and the Kreps–Scheinkman game

Wu, Xinwang; Zhu, Quantao; Sun, Laixiang

Abstract

The existing literature dealing with the equivalence between the Kreps-Scheinkman (KS) game and Cournot competition has focused on the case of a concave demand function. This paper analyses the equivalence possibilities under the much extended circumstances of strictly decreasing marginal (industrial) revenue, a twice differentiable demand function, and convex costs. It proves that in the extended context, the outcomes in the subgame perfect Nash equilibrium (SPNE) of the KS game are those of Cournot equilibrium (CE) and that a CE is on the path of the SPNE of the KS game if the marginal cost of each firm in some special (borderline) cases is not too high. It further proves that for decreasing continuous demand and strictly increasing costs, the outcome in the SPNE of the KS game (if the SPNE exists) is that of CE. Based on these results, we argue that the KS game can serve as the basic form for studying “quantity competition” and for developing a T-stage game-theoretical framework to make competition form and timing endogenous.

Citation

Wu, X., Zhu, Q., & Sun, L. (2012). On equivalence between Cournot competition and the Kreps–Scheinkman game. International Journal of Industrial Organization, 30(1), 116-125. https://doi.org/10.1016/j.ijindorg.2011.07.002

• Journal Article Type: Article
• Publication Date: Jan 1, 2012
• Deposit Date: Feb 6, 2012
• Journal: International Journal of Industrial Organization
• Print ISSN: 0167-7187
• Electronic ISSN: 1873-7986
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 1
• Pages: 116-125
• DOI: https://doi.org/10.1016/j.ijindorg.2011.07.002
• Keywords: Kreps-Scheinkman Game, Quantity Competition, Cournot Competition, Efficient Rationing Rule
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S016771871100066X