Oligopoly with Hyperbolic Demand: A Differential Game Approach

It is well known that the equilibrium solution of oligopoly games with isoelastic demand functions can be indeterminate. I revisit this issue through an open-loop differential game approach based on the assumption of sticky prices, to show that indeterminacy arises only in steady state, in the limit case where marginal costs tend to zero. Otherwise, at any time during the game, Pontryagin s Maximum Principle ensures the existence of a unique and well defined solution, irrespective of the size of marginal costs. Finally, I show that an analogous result holds in the feedback case, although the Bellman equation of the representative firm cannot be solved analytically.