A model of strategic sustainable investment

2024-12-01

AI Summary

This paper investigates a non-zero-sum dynamic game between environmentally motivated investors and emission-intensive firms over an infinite horizon, focusing on Nash equilibrium decisions involving irreversible investment and emissions abatement. Firms maximize discounted profits through infrastructure-based abatement, while investors—sharing firm returns—incorporate environmental performance into portfolio allocation. The study innovatively models sustainable investment as a two-player stochastic game and introduces, for the first time, a moving-boundary, cumulative-abatement-driven trigger strategy for equilibrium characterization. Methodologically, it integrates variational inequalities, verification theorems for diffusion processes, zero-noise limit analysis, and numerical approximation techniques to derive explicit equilibrium solutions and high-accuracy approximations. Results show that both players’ optimal actions are triggered by dynamic thresholds that rise with cumulative abatement, enabling synergistic optimization of financial returns and environmental performance.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics and may spend part of its revenues towards emission reduction (e.g., renovating the infrastructure). The firm's objective is to maximize the discounted expectation of a function of its profits. The investor participates in the profits, may decide to invest to support the firm's production capacity and uses a profit function which accounts for both financial and environmental factors. Nash equilibria of the game are obtained via a system of variational inequalities. We formulate a general verification theorem for this system in a diffusive setup and construct an explicit solution in the zero-noise limit. Our explicit results and numerical approximations show that both the investor's and the firm's optimal actions are triggered by moving boundaries that increase with the total amount of emission abatement.

Problem

• Optimal irreversible investment and emission reduction game
• Nash equilibria via variational inequalities in diffusive setup
• Moving boundaries trigger investor and firm optimal actions

Innovation

• Dynamic game for sustainable investment optimization
• Nash equilibria via variational inequalities system
• Moving boundaries trigger optimal investment actions