Solar geoengineering may lead to excessive cooling and high strategic uncertainty

The experimental evidence* strongly supports the hypothesis of free-driving behavior when each decision maker chooses its geoengineering effort. In a multilateral scenario ($N=6$), global geoengineering is near the predicted level (average 9.8 vs. predicted 10 in baseline: WSR test, P > 0.10, $n=6$). This level brings excessive cooling and lowers social surplus, which is computed as the sum of the earnings of all decision makers in an economy in a round. The realized total surplus is significantly below the socially optimal level (82%; Fig. 1; total surplus actual vs. social optimum: WSR test, P < 0.05, $n=6$), but very close to the predicted value of 87%. The social optimum prescribes a level of geoengineering that yields the median of all ideal points in the economy, not the highest one. Also in line with the predictions, the geoengineering effort in baseline is overwhelmingly undertaken by the decision makers with the highest ideal point (86% with $N=6$; SI Appendix, Figs. S2A and S3). In a multilateral scenario, the two IP10 decision makers roughly split the cost of effort to reach the desired global geoengineering level—in 37% of cases, the split was exact—and the other decision makers contribute a negligible amount (SI Appendix, Fig. S3). Additional support for the free-driving hypothesis comes from the data generated under the economies of two scenarios ($N=2$). At the economy level, global geoengineering was close to the preferred level of the decision maker with the highest ideal point (SI Appendix, Figs. S4 and S5A), who exerted most of the effort (91%; part 2). Prosocial behavior is lower than in many dictator games, most likely because 1) decision makers are teams rather than individuals (42); 2) initial endowments are equal and substantial (43); and 3) interaction is repeated (44).

Theory predicts a strategic shift when decision makers are able to countergeoengineer the climate. One effect is a geoengineering war, which occurs as those with high ideal points boost their geoengineering efforts in anticipation of those with lower ideal points counteracting them with (negative) efforts to warm temperatures. In a multilateral scenario ($N=6$), such escalation of efforts is expected to reduce social surplus to 67% of the socially optimal surplus. In terms of effort, positive and negative efforts would counteract each other, and the predicted outcome of the experiment is a temperature at the socially optimal level. The observed average global geoengineering in counter is very close to this prediction (actual of 5.97 vs. predicted of 6.00) and is significantly lower than the level of aggregate geoengineering in baseline (WMW test, P < 0.01, $n=12$; see also regressions in SI Appendix, Table S3). But this average hides a variability that has massive implications for welfare. Indeed, countergeoengineering induces a significant welfare loss: The realized social surplus in the multilateral scenario of counter is only 34% of the socially optimal level, half the predicted level of 67% (Fig. 1; total surplus vs. social optimum: WSR test, P < 0.05, $n=6$). This outcome is not, as would be expected, the result of a geoengineering war. This is less severe than predicted (Fig. 2A), with a welfare loss of only 22% of the socially optimal surplus. Rather, the driver of the poor performance is the frequent undershootings and overshootings of global geoengineering levels (Fig. 2B). Although the average global effort was close to the predicted level of six, this level was exactly achieved in only 4.4% of the cases (SI Appendix, Fig. S2B). In about 23% of cases, global geoengineering was at or below zero, and in about 16% of the cases, it was at or above 15 (SI Appendix, Fig. S2B). The variability in global geoengineering is also evident from the 95% CI shown in Fig. 1, which spans from $-4.5$ to 16.4 and is four times as wide as the corresponding interval in baseline (7.3 to 12.4). In counter, oscillations of effort in an economy across rounds were present in all economies and were wider than in baseline (average [ave.] baseline deviation from prediction is 1.8 vs. ave. counter deviation from prediction is 8.3: WMW test, P < 0.01, $n=12$; SI Appendix, Figs. S6 and S7). Thus, in counter, inefficiencies due to temperature undershooting and overshooting are greater than the inefficiencies due to the escalation of effort (44% vs. 22%; Fig. 2B and SI Appendix, Fig. S8). The first ones diminish over rounds as experience accumulates, but never vanishes.

The origin of temperature undershooting and overshooting is the strategic uncertainty characterizing the multilateral scenario of counter. The first factor generating uncertainty is the presence of many decision makers all putting nonzero effort (472 times in counter vs. 223 times in baseline; Fig. 3 and SI Appendix, Fig. S9). The second factor is the strategic interdependency of choices in counter, which is absent in baseline. Assume that some decision makers systematically deviate from the theoretical equilibrium behavior because of mistakes or in an attempt to restrain the escalation in efforts. In baseline, IP10 decision makers should react to small deviations of others, while the best reply of IP2 and IP6 decision makers would be unaffected. In counter, all decision makers need to adjust their effort level in response to others’ deviations. In the experiment, such responses played a larger role in early rounds because IP2 and IP10 were not exerting efforts at the bounds ($-15$ and 15, respectively), as theory would predict (SI Appendix, Fig. S8). Paradoxically, the losses generated by the strategic uncertainty caused by this behavior early on overshadow the potential losses from effort escalation that they were trying to avoid. Further support for this interpretation comes from the bilateral scenarios, which exhibit a drastically lower loss from overshooting and undershooting (8% in counter and 3% in baseline; Fig. 2B).

Finally, the counter condition generated a high inequality in payoffs among decision makers. The Gini index in counter was higher than in baseline (SI Appendix, Table S2), but also higher than predicted (actual of 0.31 vs. predicted of 0.25). As predicted, IP2 and IP10 decision makers had lower profits in counter compared to baseline (counter: 33 [IP2], 23 [IP10] vs. baseline: 70 [IP2], 115 [IP10]). Contrary to predictions, IP6 decision makers in counter also had lower profits than those in baseline (67 in counter vs. 109 in baseline).

Our experiment also highlights the importance of studying geoengineering in a multilateral setup. Theoretical and empirical reasons exist for going beyond a bilateral setup. In theoretical models, the strategic incentives to exert effort can substantially change, depending on the number and preferences of decision makers. Going from a bilateral to a multilateral scenario has consequences for the complexity of the coordination problem and for the equilibrium structure. For instance, our GoB game has a unique equilibrium in the bilateral scenarios and multiple equilibria in the multilateral scenario.

Experimental evidence shows that decision makers understood the change in game incentives well (Fig. 3 and SI Appendix, Tables S4–S7). First, consider baseline. In a bilateral setting, the IP10 decision maker is expected to provide the entire global geoengineering effort, while in a multilateral setting, two decision makers coordinate efforts to reach the same global geoengineering level of 10. In the experiment, the average effort of IP10 decision makers was 8.4 under $N=2$ and 4.2 under $N=6$ (significantly different at P < 0.001 according to Tobit regressions in SI Appendix, Table S6A; Fig. 3A). Next, consider counter. In a bilateral setting, the IP6 decision maker is predicted to provide an effort level of 15 if paired with IP2 or $-9$ if paired with IP10, while in a multilateral setting, two decision makers coordinate efforts to provide a global geoengineering level of six. In the experiment, the average effort of IP6 was 9.5 and $-4.7$, respectively, under $N=2$, and it was 1.1 under $N=6$ (significantly different at P < 0.01, according to Tobit regressions in SI Appendix, Table S6B; Fig. 3B). Experimental evidence also shows that moving from a bilateral to a multilateral setting in counter resulted in unexpectedly large losses stemming from the frequency of temperatures overshooting and undershooting with respect to the socially optimum level, as discussed above.

In other words, the shift in complexity affected treatments differently. In baseline, the difference in aggregate variability between the bilateral and the multilateral setups was minimal: The number of times that global geoengineering fell outside the ideal points’ range was similar in the two setups (16% vs. 22%, probit regression: P = 0.11, $n=n_{pt2}+n_{pt3}=720$ with $n_{pt1}=180$, $n_{pt1}=540$). For counter, the multilateral scenario exhibited a much higher variability in outcomes, although experience progressively reduced variability (26% vs. 52%, probit regression: P < 0.01, $n=n_{pt2}+n_{pt3}=720$ with $n_{pt1}=180$, $n_{pt1}=540$).

For both baseline and counter treatments, the optimal level of global geoengineering in $N=2$ was equal to the lowest ideal point and in $N=6$, to the median ideal point. Under $N=2$, this yielded a total surplus of 252 (IP2 and IP6), 212 (IP2 and IP10), and 236 (IP6 and IP10), and, under $N=6$, a total surplus of 716 (IP2, IP6, and IP10). Under $N=6$, the predicted Gini index of inequality reaches a minimum of 0.07 if effort is equally split by the two IP6 decision makers.

In baseline, all types of economies admit a unique subgame perfect Nash equilibrium outcome: Global geoengineering equals the highest ideal point in the economy. Under $N=2$, the decision maker with the highest ideal point contributes all of the effort, and the other decision maker puts in zero. Under $N=6$, the two IP10 decision makers put in a total effort equal to 10. The predicted outcome is suboptimal relative to the total surplus from the social optimum: 94% for economy (IP2 and IP6), 85% for economy (IP2 and IP10), 93% for economy (IP6 and IP10), and 87% for economy of six. Inequality, as measured by the Gini index, is 0.03 for economy (IP2 and IP6), 0.11 for economy (IP2 and IP10), 0 for economy (IP6 and IP10), and 0.13 for the economy of six (when IP10 decision makers produce five each).

In counter, global geoengineering equals the lowest ideal point of the decision makers in $N=2$ and the median ideal point of the decision makers in $N=6$. In $N=2$, the decision maker with the higher ideal point contributes the maximum amount of effort, while the decision maker with the lower ideal point counteracts this effort and brings it down to its own ideal level. In $N=6$, IP10 decision makers put in 15, IP2 decision makers put in $-15$, and IP6 decision makers put in a total of six. Counter leads to a level of global geoengineering equivalent to the socially optimal one, but the resulting total surplus is not the same; that is, countries’ efforts are wasted, as ${\sum }_{j\ne i}\left|g_{j,i}\right|\gg G$. In $N=2$, this sum is 26 for economies (IP2 and IP6) and (IP2 and IP10) and 24 for (IP6 and IP10). In $N=6$, this sum is 66, resulting in a total surplus of just 66% of the socially optimal surplus and an inequality of 0.25 (when IP6 decision makers produce three each).

A summary of these theoretical predictions is available in SI Appendix, Table S1. The formal proofs for a general $N$ is available in SI Appendix, Proof of Theoretical Predictions. We also report theoretical analyses of two model extensions in SI Appendix, Robustness of Theoretical Results to Variations of the Model Assumptions): allowing quadratic instead of linear damages and taking away the upper bound of effort. Predictions are qualitatively similar.

All relevant data and code are included in the manuscript, SI Appendix, and Datasets S1–S4.