Consider a Bertrand model in which each firm may be inactive with a known probability, so the number of active firms is uncertain. This simple model has a mixed-strategy equilibrium in which industry profits are positive and decline with the number of firms, the same features which make the Cournot model attractive. Unlike in a Cournot model with similar incomplete information, Bertrand profits always ncrease in the probability other firms are inactive. Profits decline more sharply than in the Cournot model, and the pattern is similar to that found by Bresnahan & Reiss (1991).

Bertrand model, Cournot model, incomplete information, uncertainty
Tinbergen Institute Discussion Paper Series
Tinbergen Institute

Janssen, M.C.W, & Rasmusen, E. (1998). Bertrand Competition under Uncertainty (No. TI 98-083/1). Tinbergen Institute Discussion Paper Series. Retrieved from