Bertrand Competition Under Uncertainty

Consider a Bertrand model in which each rm may be inactive with a known probability, so the number of active rms is uncertain. This activity level can be endogenized in any of several ways{ as whether to incur a xed cost of activity, as output choice, or as quality choice. Our model has a mixed-strategy equilibrium, in which industry pro ts are positive and decline with the number of rms, the same features which make the Cournot model attractive. Unlike in a Cournot model with similar incomplete information, Bertrand pro ts always increase in the probability other rms are inactive. Pro ts decline more sharply than in the Cournot model, and the pattern is similar to that found empirically by Bresnahan & Reiss (1991). Janssen: Department of Economics, H7-22, Erasmus University, 3000 DR Rotterdam, The Netherlands. Fax: 31-10-4081949. [email protected]. Rasmusen: Professor of Business Economics and Public Policy and Sanjay Subhedar Faculty Fellow, Indiana University, Kelley School of Business, BU 456, 1309 East 10th Street, Bloomington, Indiana, 47405-1701. (812) 855-9219. Fax: 812-855-3354. [email protected]. Http://Php.indiana.edu/ erasmuse. Copies of this paper can be found at Www.bus.indiana.edu/ erasmuse/@Articles/Unpublished/bertrand.pdf. We thank David Schmidt and participants in seminars at the Indiana University Dept. of Economics, Erasmus University and CIRANO in Montreal for their comments.