This paper provides a tractable empirical framework to analyze firm behavior in a dynamic oligopoly when demand is declining over time. I modify Fudenberg and Tirole (1986).s model of exit in a duopoly with incomplete information to a model that can be used in an oligopoly, and combine this with an auxiliary entry model to address the initial conditions problem. I estimate this model with panel data on the U.S. movie theater industry from 1949 to 1955, using variations in TV diffusion rates across households, market structure before the exit game starts, and other market characteristics to identify the parameters in the theater's payoff function and the distribution of unobservable fixed costs. Using the estimated model, I measure strategic delays in the exit process due to oligopolistic competition and incomplete information. The delay in exit that arises from strategic interaction is 2.7 years on average. Out of these years, 3.7% of this delay is accounted for by incomplete information, while the remaining 96.3% is explained by oligopolistic competition.