An integral transformation approach to differential games: a climate model application

TL;DR

This paper introduces an Integral Transformation Method (ITM) for solving optimal control and differential game models, demonstrated on a climate model to analyze emissions, welfare, and uncertainty impacts.

Contribution

The paper presents a novel ITM that simplifies solving linear dynamic control problems and applies it to climate models for equilibrium and robustness analysis.

Findings

Computed Nash equilibria for climate policy scenarios

Compared equilibria to efficiency benchmarks

Analyzed impact of deep uncertainty on climate outcomes

Abstract

We develop an Integral Transformation Method (ITM) for the study of suitable optimal control and differential game models. This allows for a solution to such dynamic problems to be found through solving a family of optimization problems parametrized by time. The method is quite flexible, and it can be used in several economic applications where the state equation and the objective functional are linear in a state variable. We illustrate the ITM in the context of a two-country integrated assessment climate model. We characterize emissions, consumption, transfers, and welfare by computing the Nash equilibria of the associated dynamic game. We then compare them to efficiency benchmarks. Further, we apply the ITM in a robust control setup, where we investigate how (deep) uncertainty affects climate outcomes.