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 activity level can be endogenized in several ways ---whether to incur a fixed cost of activity, for example, or what level of output to choose. Our 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 increase in the probability other firms are inactive. Profits decline more sharply than in the Cournot model, and the pattern is similar to that found empirically by Bresnahan and Reiss (1991).
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