  One of the most widely used models for studying the geographical economics of
climate change is the Regional Integrated model of Climate and the Economy
(RICE). In this paper, we investigate how cooperation and competition arise in
regional climate policies under the RICE framework from the standpoints of game
theory and optimal control. First, we show that the RICE model is inherently a
dynamic game. Second, we study both cooperative and non-cooperative solutions
to this RICE dynamic game. In cooperative settings, we investigate the global
social welfare equilibrium that maximizes the weighted and cumulative social
welfare across regions. We next divide the regions into two clusters: developed
and developing, and look at the social welfare frontier under the notion of
Pareto optimality. We also present a receding horizon approach to approximate
the global social welfare equilibrium for robustness and computational
efficiency. For non-cooperative settings, we study best-response dynamics and
open-loop Nash equilibrium of the RICE game. A Recursive Best-response
Algorithm for Dynamic Games (RBA-DG) is proposed to describe the sequences of
best-response decisions for dynamic games, which indicates convergence to
open-loop Nash equilibrium when applied to the RICE game by numerical studies.
We also study online receding horizon feedback decisions of the RICE game. A
Receding Horizon Feedback Algorithm for Dynamic Games (RHFA-DG) is proposed.
All these proposed solution concepts are implemented and open sourced using the
latest updated parameters and data. The results reveal how game theory may be
used to facilitate international negotiations towards consensus on regional
climate-change mitigation policies, as well as how cooperative and competitive
regional relations shape climate change for our future.
