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

Abstract

We characterise the subgame perfect equilibrium of a differential market game with hyperbolic inverse demand where …firms are quantity-setters and accumulate capacity over time à la Ramsey. The related Hamilton-Jacobi-Bellman are solved in closed form both on infi…nite and on …finite horizon setups and the optimal strategies are determined. Then, we analyse the feasibility of horizontal mergers in both static and dynamic settings, and …find appropriate conditions for their profi…tability under both circumstances. Static pro…fitability of a merger implies dynamic profi…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.

Keywords: capacity, differential game, Markov-perfect equilibrium, Hamilton-Jacobi-Bellman equation, horizontal mergers

JEL Classification: C73, L13