A Dynamic Multi-Objective Duopoly Game with Capital Accumulation and Pollution

Abstract

This paper studies a discrete-time dynamic duopoly game with homogenous goods. Both firms have to decide on investment where investment increases production capacity so that they are able to put a larger quantity on the market. The downside, however, is that a larger quantity raises pollution. The firms have multiple objectives in the sense that each one maximizes the discounted profit stream and appreciates a clean environment as well. We obtain some surprising results. First, where it is known from the continuous-time differential game literature that firms invest more under a feedback information structure compared to an open-loop one, we detect scenarios where the opposite holds. Second, in a feedback Nash equilibrium, capital stock is more sensitive to environmental appreciation than in the open-loop case.