Geoengineering and global warming: a strategic perspective

Abstract

If major emitters fail to mitigate global warming, they may have to resort to geoengineering techniques that deflect sunlight from planet Earth and remove carbon dioxide from the atmosphere. In this article, I develop a strategic theory of geoengineering. I emphasize two key features of geoengineering. First, whereas emissions reductions can be mandated now, geoengineering techniques are only available in the future. Second, major powers can unilaterally implement geoengineering projects that may hurt other countries. My game-theoretic analysis demonstrates that unilateral geoengineering presents a difficult governance problem if it produces negative externalities in foreign countries. Interestingly, countries may be tempted to reduce emissions now, so as to prevent a harmful geoengineering race in the future. The theoretical results can help scholars and policymakers understand the relationship between climate mitigation and geoengineering.

Appendix: Model extensions

1.1 Discounting the future

Since the cost of geoengineering is incurred in the future, it seems plausible to assume that states could discount the costs and benefits of geoengineering. Given this, suppose each country i discounts future payoffs by a factor of $\delta\in(0,1).$ With most climate damages occurring in the future, country i now maximizes

$$ U_{i}=B\cdot {\hbox{ln}}(E_{i})-\delta\cdot\left[C\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

By the expected utility theorem, maximizing U _i is equivalent to maximizing

$$ \tilde{U_{i}}=\frac{B}{\delta}\cdot {\hbox{ln}}(E_{i})-\left[C\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

Writing $\tilde{B}=\frac{B}{\delta}$ and solving as in the main text, all results continue to hold. With $\delta\in(0,1),$ the primary implication of discounting is that as δ decreases, both emissions E ^* _i and geoengineering G ^* _i increase.

1.2 Uncertainty

Suppose that the cost of geoengineering is subject to uncertainty. In particular, assume the respective costs of domestic and foreign geoengineering are G ² _i and $x\cdot G_{j}^{2}$ with probability $\rho\in(0,1).$ With the complementary probability 1−ρ, these costs are assumed not to exist. The governments are aware of the prior probability ρ, but the actual existence of the costs is assumed to be subject to uncertainty, as indicated in the geoengineering literature (Victor 2008; Virgoe 2009). Now, the government of country i maximizes

$$ U_{i}=B\cdot {\hbox{ln}}(E_{i})-C\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-\rho\cdot\left[G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

Again by the expected utility theorem, the maximization problem is identical to

$$ \tilde{U}_{i}=\frac{B}{\rho}\cdot {\hbox{ln}}(E_{i})-\frac{C}{\rho}\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-\left[G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

Writing and $\tilde{C}=\frac{C}{\rho},$ the analysis in the main text can be replicated without modifications. The effect of increasing ρ on emissions E ^* _i , E ^* _j and geoengineering G ^* _i , G ^* _j is ambiguous and depends on the ratio of B to C.

1.3 Asymmetric damages within countries

Suppose that in each country i, two groups labeled by αⁱ, βⁱ exist. Suppose that the damages from geoengineering are asymmetric across the groups. For group αⁱ, the cost of geoengineering is multiplied by a factor α > 0. For group βⁱ, the multiplier is β > 0. Now the government of country i is assumed to maximize

$$ U_{i}=B\cdot {\hbox{ln}}(E_{i})-C\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-\left(\alpha+\beta\right)\cdot\left[G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

Again by the expected utility theorem, this is equivalent to maximizing

$$ \tilde{U}_{i}=\frac{B}{\alpha+\beta}\cdot {\hbox{ln}}(E_{i})-\frac{C}{\alpha+\beta}\cdot(E_{i}+E_{j}-G_{i}-G_{j})^{2}-\left[G_{i}^{2}-x\cdot G_{j}^{2}\right]. $$

Writing $\tilde{B}=\frac{B}{\alpha+\beta}$ and $\tilde{C}=\frac{B}{\alpha+\beta},$ the analysis in the main text can be replicated. As α or β increases, the changes in emissions E ^* _i , E ^* _j and geoengineering G ^* _i , G ^* _j are ambiguous and depend on the ratio of B–C.