Bertrand Competition under Uncertainty

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).