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.
Highlights
Corporate social responsibility (CSR) emphasizes that a firm does not just care about profit maximization, but has at the same time other objectives in mind that benefit society.According to Wirl et al [1], examples of CSR projects are environmental reports, philanthropic support and sponsoring, energy and environmental management, mentoring and educational programs for workers, family-friendly workplaces and more
We obtain the new result that, compared to an open-loop information structure, in a feedback Nash equilibrium the firms are less sensitive to changes in environmental appreciation
The proposition follows from the comparison of the long-run value C of the capital stock in the open-loop Nash equilibria given by Equation (26) and the long-run value C 00 of the capital stock in the cooperative equilibrium given by Equation (139)
Summary
Corporate social responsibility (CSR) emphasizes that a firm does not just care about profit maximization, but has at the same time other objectives in mind that benefit society. Our approach is close to albeit different from that of Rettieva [5] She considers a dynamic, discrete time, two-player game model where the players use a common resource. Our paper is connected to the work of Crettez and Hayek (2021) [9] who study a dynamic Cournot duopoly where production causes pollution, albeit without capital accumulation. They notably show that contrary to the case where the firms’ objective just concerns profit maximization, there exist Nash equilibria where production is lower than in the cooperative equilibrium. In this measure future values of pollution are discounted at the same rate as future receipts
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