Bertrand Competition Without Completely Certain Production

Janssen and Rasmusen (2002) show that a Bertrand model with an uncertain number of firms has only one symmetric equilibrium, and profits in that equilibrium fit the empirical data in Bresnahan and Reiss (1991). However, unless its equilibrium is unique, Janssen and Rasmusen's model cannot be said to predict that data. This paper establishes uniqueness in their most general model. It also shows that as each firm's probability of being active approaches 1, the model converges to Bertrand except that the percentage effect of merger on profits (and also, at least in the linear case, on prices) grows without bound