We study duopolistic competition in a homogeneous good through time under the assumption that its current desirability is an exponentially weighted function of accumulated past consumption. This implies that the current price of the good does not decline by as much to accommodate any given level of current consumption as it would if its desirability were a function solely of present consumption. We analyze the consequences of this "stickness" of the goods's current price through a speed of adjustment parameter that yields instantaneous adjustment as a limiting case. Our analysis is conducted in terms of a differential game. The open-loop and closed-loop Nash equilibrium strategies are derived, from which the corresponding asymptotically stable steady-state equilibrium prices for the good are obtained. These equilibrium prices are then analyzed as the speed of price adjustment becomes instantaneous. It is found that the equilibrium price corresponding to the open-loop Nash equilibrium strategies approaches the static Cournot equilibrium price while the equilibrium price corresponding to the close-loop Nash equilibrium strategies, which are subgame perfect, approaches a price below it.