A Dynamic Multi-Objective Duopoly Game with Environmentally Concerned Firms

Abstract

Social pressures, in addition to the law, incite more and more firms to pursue multiple and separate objectives. This trend raises the following question: will the change in the number of objectives pursued by firms affect their strategic interactions? To address this issue we focus on a dynamic duopoly where each firm has two objectives: one of the firms’ objectives is financial and the other is environmental. Production is a polluting activity and the actual level of pollution depends on current and past emissions. We analyze both open-loop Nash and cooperative equilibria (these equilibria are also trivially feedback as the equilibrium strategies are constant). We show that contrary to the case where firms’ unique objective is the financial one, there are Nash equilibria where production is lower than in the cooperative equilibrium. This stems from the fact that in a Nash equilibrium firms do not coordinate the choice of the relative weight given to the environmental objective. We obtain the same conclusion when firms can mitigate pollution. In this case, we also show that there are Nash equilibria where the sum of the firms’ mitigation efforts is higher than its value in the cooperative equilibrium.

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

“…Due to this, they can reduce their production more than in the cooperative case. This result extends the findings of Crettez and Hayek [9] to the case where firms accumulate capital.…”

“…Therefore, we always have ∂K 1t ∂λ 2 < 0. Notice that this is in contrast with the model without capital accumulation of Crettez and Hayek [9] where a change in λ 2 has an indeterminate effect on the production level.…”

“…Our paper is also 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 paper, we also obtain this form of over-compliance. Here, however, open-loop equilibria differ from feedback equilibria, whereas in the work of Crettez and Hayek [9], open-loop equilibria are all feedback.…”

Generalized model of stochastic common property fishery differential game: Numerical study

“…Dynamic game models of exploitation of natural resource were considered by Munro [36]; Levhari and Mirman [28]; Clark [16] and Long [30]. There are many papers investigated the problem of extraction of a common property (Lewis, and Schmalensee [29]; Loury [31]; Dockner et al [20]; Salo and Tahvonen [46]; Benchekroun ([6,7]); Benchekroun [8]; Breton et al [11]; Mazalov et al [32]; Crettez, and Hayek [17]; Parilina, and Zaccour [43]. Stochastic differential game problems (SDGPs) have many applications in modelling and analysing of real-world situations such as renewable resource extraction problem [19,50].…”