AbstractThis paper is concerned with the optimal output decisions of a dominant firm in the presence of imperfect information about the rival's reactions. The model is multi‐period with the profits in each period being independent of those in other periods. Consequently, if the rival's reaction parameter were known to the dominant firm, a myopic policy would be optimal, In the presence of imperfect information about the rival's unknown reaction parameter, the dominant firm acts in a Bayesian manner by updating its prior distribution based on the observations of the rival's outputs. Because of the multiplicative shape of the rival's reaction function, the Bayesian updating rule is a function of the dominant firm's decision variable, i.e. its output decisions. This creates a dependence of the future value of the dominant firm on the present output decision, and hence a myopic policy is not, in general, optimal. It is shown that through output experimentation the dominant firm will tend to overproduce and, consequently, will increase its expected discounted profits (market value