Oligopoly with Hyperbolic Demand: A Differential Game Approach

2008) and an anonymous referee for very insightful comments and suggestions. The usual disclaimer applies. Financial support form the University of Bologna (Pro-getto Strategico “Strumenti di supporto alle decisioni dei produttori ed operatori del mercato dell’energia elettrica”) is gratefully acknowledged. Convex demand functions, although commonly used in consumer theory and in accordance with a large amount of empirical evidence, are known to be problematic in the analysis of firms ’ behaviour and therefore rarely used in oligopoly theory, due to the possible lack of concavity of firms ’ profit functions and the indeterminacy arising in the limit as marginal costs tend to zero. Here I investigate a dynamic oligopoly model with hyperbolic demand and sticky price, characterising the open-loop optimal control and the related steady state equilibrium, to show that the indeterminacy associated with the limit of static model is indeed confined to the steady state of the dynamic one, while the latter allows for a well-behaved solution at any time during the game. Although the feedback solution cannot be analytically attained since the model is not built in linear-quadratic form, I show that analogous considerations also apply to the Bellman equation of the individual firm