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

• Main Authors: Bertrand Crettez, Naila Hayek, Peter M. Kort
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Mathematics
• Subjects: game theory; corporate environmentalism; dynamic multi-objective duopoly; open-loop equilibrium; feedback Nash equilibrium
• Online Access: https://www.mdpi.com/2227-7390/9/16/1983

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.