Bertrand Crettez – Université Panthéon-Assas, Paris II, France
We analyze a differential game of capital accumulation in the Cournot duopoly model of complements. In this model, consumers have a downward-sloping demand for a final product which is made out of n different complement goods. The _rms producing these goods accumulate capital and set their prices facing capacity constraints. It turns out that in the price equilibrium, firms' instant profits are discontinuous functions of their capacities. As a consequence, one cannot use standard optimal control approaches to study the equilibria of the dynamic game. We nevertheless find that in contrast with the literature on capital accumulation games the open-loop Nash equilibrium does not exist generally. Existence of equilibrium only holds when firms cannot disinvest and have the same initial production capacity.
(With Naila Hayek and Guiomar Martín-Herrán)