Dynamic Duopoly under Demand Uncertainty

Abstract

Demand uncertainty is introduced into a dynamic model of duopoly. In the face of this uncertainty each firm is unable to observe its rival's previous period's output. Its strategy is contingent, therefore, on its own last period's output and on the last period's price. The sole Nash equilibrium is a repetition of the equilibrium in the one-period problem. This paper introduces demand uncertainty into a dynamic model of oligopoly.' Each firm is assumed to be ignorant of its rival's preceding outputs and to observe only previous prices. Thus each firm's strategy is contingent upon its own last period's output and on last period's price. Similar static models have been used to examine how such uncertainty might limit the implicit collusion of oligopolists. (See, e.g., Stigler, 1964 and Spence, 1978.) In the present paper demand uncertainty implies that each firm's strategy will be put to the test (i.e., multiple values of the relevant independent variables must occur). It is required, by definition, that each firm behave in accordance with its own strategy, and that this constitute a best-reply to its rival's strategy. This contrasts with the static (pedagogic) model of oligopoly in which 'actions' and 'reactions' are apparently instantaneous. In addition, the equilibrium attained, though dependent on each firm's 'conjectures' concerning its rivals' behaviour, does not require each firm to live up to the other firms' conjectures. The present more stringent requirement rules out the possibility arising in the static model that firms be 'right for the wrong reason,' to use Fellner's (1949) phrase. In the simple