On the Feedback Solutions of Di erential Oligopoly Games with Hyperbolic Demand Curve and Capacity Accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a di erential Cournot game with hyperbolic inverse demand, where rms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterised via the Hamilton-Jacobi-Bellman equations solved in closed form both on in nite and on nite horizon setups. To illustrate the applicability of our model and its implications, we analyse the feasibility of horizontal mergers in both static and dynamic settings, and nd appropriate conditions for their pro tability under both circumstances. Static pro tability of a merger implies dynamic pro tability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand. JEL Classi cation: C73, L13