On the Existence of Bayesian Cournot Equilibrium

Abstract

Acknowledgements: The authors are indebted to an anonymous referee for insightful suggestions that greatly improved the presentation of our results. These suggestions helped us both to better position our work in the general context, and to provide a sharper insight into the source of non-existence of a Bayesian Cournot equilibrium in the examples presented in Section 3.The authors also gratefully acknowledge …nancial support of the Spanish Ministry of Education, grant SEJ2007-67436. 1 Hitotsubashi Universiry Economics Discussion Paper Series No. 2008-11 AbstractWe show that when …rms have incomplete information about the market demand and their costs, a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. In fact, we are able to construct surprisingly simple and robust examples of duopolies with these features. However, we also …nd some su¢ cient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries.More general results arise when negative prices are possible.

Ambiguity and price competition

“…The latter remains an under-developed topic, partly due to the well-known technical tensions that arise when working with discontinuous payoffs, ambiguity and asymmetric information in competition. 10 For instance, only recently has the issue of equilibrium existence under incomplete information in a Cournot oligopoly, even with continuous payoffs, been addressed by Einy et al (2010).…”

“…The disruptive effects of incomplete information are not confined to price competition. Einy et al (2010) consider Bayesian output-setting oligopolists with incomplete information regarding state-contingent production costs and market demand. They provide conditions for the existence and uniqueness of pure strategy Nash equilibrium without permitting negative prices.…”

Price Discrimination in Dynamic Cournot Competition

“…Since Cournot dynamic competition is related to the behavior of consumers, expectations of manufacturer demands, the number of oligopolists, and so on, there are extensive works from different points of view to study Cournot competition. For instance, see the complexity of solutions for Cournot duopoly [2][3][4][5] and Cournot games with three oligopolists [6], and see Cournot competition with incomplete information [7][8][9]. In [10,11], Guirao and Rubio introduced Cournot-like models by generalizing Cournot duopoly to players.…”

Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems

“…Generally, there are no good methods for solving such systems, even in the simple case of only two equations of the form: 1 ( 1 , 2 ) = 0 and 2 ( 1 , 2 ) = 0; see van der Laan et al [14]. Thus, some existing theorems of zero points or fixed points had been extensively established by a number of authors; see [1,2,4,[10][11][12][13][15][16][17][18][19][20][21][22][23] and so forth.…”