Exploitation of a Productive Asset in the Presence of Strategic Behavior and Pollution Externalities

Abstract

We study the strategic behavior of firms competing in the exploitation of a common-access productive asset, in the presence of pollution externalities. We consider a differential game with two state variables (asset stock and pollution stock), and by using a piecewise-linear approximation of the nonlinear asset growth function, we provide a tractable characterization of the symmetric feedback–Nash equilibrium with asymptotically stable steady state(s). The results show that the firm’s strategy takes three forms depending on the pair of state variables and that different options for the model parameters lead to contrasting outcomes in both the short- and long-run equilibria.

Dynamic Multicriteria Game with Pollution Externalities

“…The recent contributions [19][20][21] considered the exploitation of a productive asset under pollution externalities and strategic behavior. Zaccour et al [19] assumed that harvesting activities damage the environment and the resource growth rate depends on the accumulated pollution.…”

“…The recent contributions [19][20][21] considered the exploitation of a productive asset under pollution externalities and strategic behavior. Zaccour et al [19] assumed that harvesting activities damage the environment and the resource growth rate depends on the accumulated pollution. For the model with many players maximizing welfare over an infinite planning horizon, the authors constructed noncooperative and cooperative equilibria.…”

Dynamic Stackelberg duopoly with sticky prices and a myopic follower

“…Some difficulties may appear even in such optimal control problems, like e.g., in , where the solution is piecewiselinear with infinitely many pieces and the standard undetermined coefficient method returns a control far from the unique optimum. Nevertheless, such complications does not have to happen always in this kind of problems: there is a sequence of works, with piecewise linear dynamics in which this problem does not appear at a Nash equilibrium: Benchekroun (2008), Benchekroun et al (2020), Vardar and Zaccour (2020), or at a Stackelberg equilibrium: Colombo and Labrecciosa (2019).…”