Strategic logic of unilateral climate intervention

Climate change and unabated greenhouse gas emissions are increasing the possibility that the world will turn to climate intervention to curb ever-increasing global temperatures. This paper uses game theory to elucidate the conditions that might make a state more or less likely to begin unilateral, as opposed to internationally coordinated, climate intervention (UCI). We solve this game for several specific scientific, economic, and climatological conditions that change the likelihood of a government starting its own climate intervention deployment program without the participation of the broader international community. Specifically, we demonstrate that the plausibility of UCI is linked to perceptions of three key elements: (1) the effectiveness of climate intervention strategies, (2) the sensitivity of specific governments to punishment by other states, and (3) satisfaction with climate and weather in the present. We conclude by discussing how this formal game theory model informs the design of future Earth system model simulations of UCI, international agreements related to climate intervention, and the development of solar climate intervention technologies.


Introduction
Climate change is unfolding in the present as humanity continues unabated greenhouse gas emissions globally (Masson-Delmotte et al 2021).Extreme heat and precipitation events, disastrous flooding, and sea level rise are realities in the present and increasingly provide a window into the future of environmental disasters (Davenport et al 2021).Despite this, policy commitments are consistent with a world that will likely warm by a global mean of at least 2 • C globally (SEI et al 2021, Diffenbaugh andBarnes 2023).Moreover, those policy commitments are falling far short of what is needed to minimize temperature increases and avoid potentially dangerous Earth system change (Armstrong Mckay et al 2022).
If temperatures become intolerable, there will be interest in finding ways to avoid the most dangerous impacts of climate change.One such method could be solar climate intervention (SCI) (Burns et al 2016).Broadly speaking, SCI refers to the process of deliberately reflecting more of the sun's energy back to space (Keith 2020).The most widely researched approach to global SCI is stratospheric aerosol injection (SAI), which would involve the dispersal of aerosols in the Earth's stratosphere (NASEM 2021).While there is currently no active SAI deployment program, increased research attention to SAI suggests a need for wide-ranging scenarios that explore numerous possibilities of both the rationale of how SAI may be pursued, and the associated consequences for the destabilizing climate system (Kravitz et al 2015, MacMartin et al 2022)).
It is very widely acknowledged that a successful SAI program would require interdisciplinary attention to climate system modeling (Tilmes et al 2018, MacMartin et al 2022, Visioni et al 2023), deployment technology (Smith and Wagner 2018), and the development of an equitable regime to govern a future SAI program (Horton and Reynolds 2016, Parson andReynolds 2021, Lockley et al 2022).However, these lines of inquiry do not always advance in concert with each other.SAI simulations have significantly improved our understanding of how deployment of various chemicals at various latitudes, altitudes, seasons, and quantities might produce different outcomes.But these insights are generated by focusing on SAI as an apolitical engineering problem (e.g.Kravitz et al 2017, Zhang et al 2022), while setting aside questions about how a single technocratic authority would overcome the significant geopolitical and legal barriers to running a program at the ideal latitudes and altitudes.Scientific feasibility and geopolitical plausibility are not one and the same, but both are critical prerequisites to a well-designed SAI program.
The central contention of this paper is that simulations have given the expert community an improved understanding of the physical science and possible impacts of SAI, but this knowledge rests on tacit assumptions about international relations that demand further exploration.Specifically, geopolitical competition, international laws governing the use of airspace, the division of global airspace into hundreds of separate jurisdictions, and concerns about sharing military technology may all challenge the plausibility of an SAI program that calls for controlled deployment across sixty or more degrees of latitude (e.g.Tilmes et al 2018, Weisenstein et al 2022, Visioni et al 2023).Simulations run on carefully controlled SAI deployment at, say, 30 N, 15 N, the equator, 15 S, and 30 S along the 180E meridian reveal much about the technical feasibility of designing SAI for desired, predetermined outcomes, but these models do not typically engage in questions about who, if anyone, could possibly do this in a coordinated fashion along a 4000 mile vector across the remote Pacific Ocean.
The costs of climate intervention are now such that an individual state could act alone in its own region (Eliason 2021), even if that means SAI is not implemented across the surface of the globe (or at least across a very wide range of latitudes) as it is commonly modeled in existing simulation-based research (Kravitz et al 2017, Tilmes et al 2018, MacMartin et al 2022, Richter et al 2022).This is the so-called 'freedriver' problem, whereby a single actor (or limited set of actors) could affect the entire Earth system (Heyen et al 2019).Detailed, technical analysis of the costs and logistics associated with a continuous program of SAI deployment indicates an SAI program could be initiated with modifications to existing technology and a budget of $5 billion per year or less (Smith and Wagner 2018).A primary conclusion of this work is that, relative to global costs of decarbonization, maintaining a globally-effective SAI program is notably inexpensive.
There is, therefore, a divergence between simulations of globally dispersed (yet centrally controlled) SAI scenarios versus the geopolitical realities that might drive states toward unilateral climate intervention (UCI) in their own regions.While climate simulations have implicitly assumed centrally-controlled SAI deployment over a large swath of the Earth's surface, it is also possible that SAI will instead be pursued unilaterally over a much smaller geographic space (Rabitz 2016).This divergence creates an urgent need for tools with which we can rigorously explore the potential for unilateral, geographically confined SAI programs that bear little resemblance to some of the idealized simulations that inform our present scientific understanding of SAI outcomes.
Game theory is a useful tool for formally describing and modeling how a certain set of assumptions about state actions, beliefs, and available strategies could lead to a decision like UCI (Urpelainen 2012, Heyen et al 2019).Unlike individual narrative explanations for UCI, creating and solving a simplified UCI game allows us to identify conditions that might make different UCI outcomes-including, for example, sanctions, continued UCI, or a decision to start and stop UCI-more or less likely.Such an analysis would provide new theoretical insight, both into the types of actors that might pursue UCI, as well as the types of strategic interactions that could unfold following the initiation of UCI.Importantly, it could also point to specific international actions that could make lone states much more or less likely to experiment with UCI in the future.Such insights will be increasingly important as global temperatures and the frequency of climate-related disasters rise.
Formal models are not predictions of the future and they cannot represent the complexity of climatological and political systems.They can, however, reduce strategic decisions to their base elements and produce logical implications that can be leveraged to understand what might affect the decision to pursue UCI, including beliefs about the future, vulnerability to punishment from other states, and satisfaction with weather in the status quo.Furthermore, this method has already been used to explore what might cause some states to attempt to 'counter-geoengineer' if others' climate interventions are not to their liking (Urpelainen 2012, Heyen et al 2019) or incentivize the formation of regional pro-climate intervention coalitions (Moreno-Cruz et al 2012, Ricke et al 2013).This paper seeks to expand this literature by homing in on the risky decision to unilaterally initiate a climate intervention program with uncertain global effects.
The next section introduces a novel two-player UCI game and is followed by solutions to the game.The paper concludes with a discussion of the limitations of the analysis and specific implications for climate intervention and international environmental governance.

Formal model
This section sets-up the game, and the solution is provided in the following section.Imagine a simplified model of the world in which one state, an Initiator, possesses the ability to begin UCI and another state, the Respondent, must then choose to either stand by or punish the Initiator, perhaps through economic or military sanctions.We can model the conditions that might compel the Initiator to use UCI with a three-move game, which is depicted in the extensive form in figure 1.
The game begins when the Initiator decides to start UCI (g) or not (∼ g).If the Initiator does not use UCI, the game is over and both states receive the climate in the status quo path indefinitely3 .The payoffs for this outcome are represented mathematically by the terms wI (1−δI) and wR (1−δR) , with the desirability of each state's climate unaltered by UCI (w I and w R ) ranging from 0 to 1. Future payoffs are calculated by dividing by the term 1 − δ, where δ ranges from 0 to 1 and represents the extent to which each state discounts payoffs in the future vis-à-vis the present.States with a higher δ place more value in the future, while states with a lower δ are primarily concerned with the present and care relatively less about longterm costs or benefits.This is the standard notation for representing future payoffs in game theoretic modeling (Gibbons 1992).
Should the Initiator begin UCI, it suffers the cost of c.This cost can represent any combination of financial and non-pecuniary penalties that the Initiator must endure should it choose UCI (g).UCI also creates altered climate conditions for the Initiator and the Respondent, represented by g I and g R .These outcomes could be better or worse than climate in the status quo (w I and w R ), so let each of these terms range independently from each other between −1 and 1.The Initiator's payoff for UCI in a single period, independent from the reactions of other states, is therefore g I − c.The Respondent does not pay the costs of UCI, so it receives g R .
Due to the complexity of the global climate, the values of g I and g R are unknown until UCI is attempted at scale.To model this revelation of new information, we follow the game theoretic literature (Gibbons 1992) by allowing an entity called Nature to randomly define and reveal the heretofore unknown values of g I and g R after and only if the Initiator decides to use UCI.This reveal effectively divides the game into two parts.After Nature reveals the true effects of UCI, the Initiator and Respondent act with complete information about UCI and perfect knowledge about its own and the other state's payoffs.Before Nature's reveal, the Initiator must decide whether it will initiate with beliefs about UCI, but crucially, no concrete knowledge of the outcomes of its decision to initiate UCI4 .
After Nature reveals g I and g R , each state has one decision left to make.First, allow the Respondent to experience the effects of UCI and then decide whether to punish (p) or not punish (∼ p) the Initiator.Punishment-used interchangeably with 'sanctions' below-imposes costs equal to x on the Initiator, but the act is not costless for the punisher.The Respondent suffers costs equal to s when it applies sanctions.After all, the implementation of sanctions entails costs on countries that must now mobilize their militaries or suffer from decreased or less efficient international trade (Martin 1993).If the Respondent applies sanctions, the Initiator's payoff for using UCI at a given time decreases to g I − c − x.Meanwhile, the Respondent receives a payoff of g R for that time period if it does not apply sanctions or g R − s for that time period if it does.Whether these payoffs are indefinite into the future, and thus divided by 1 − δ, depends on what the Initiator chooses to do in the game's final move.
The game ends when the Initiator decides what it will do after observing the true outcome of UCI and the Respondent's willingness to punish.Having made these observations, the Initiator can decide to cease UCI (∼g) or continue it indefinitely into the future (g ′ ).When UCI is continued into the future, the payoffs described above are divided by 1 − δ I for the Initiator and 1 − δ R for the Respondent.However, when UCI is stopped, states receive the payoffs for UCI only once and then return to the status quo payoffs of wI (1−δI) and wR (1−δR) .

Solutions
We solve the game for subgame perfect Nash equilibria through backwards induction by starting with the final decision and determining what each player would do, assuming earlier decisions were to deliver a player to that decision node.By doing so, we can identify the sets of conditions that allow each of the outcomes listed above to occur, given each state's payoffs and beliefs at each stage of the game (Gibbons 1992).A technical solution is provided in the supplementary appendix, while the main text outlines the basic logic of the game and summarizes the principal implications.Most importantly, we identify important thresholds linked to the outcome of UCI both for the Initiator (g I ) and the Respondent (g R ).
Beginning first with the Initiator's final decision at the end of the game, we identify two thresholds, which we shall label g L I and g H I and define as follows: When Nature reveals that g I is less than the threshold defined as g L I , then the Initiator will stop UCI in the second period regardless of whether it is punished.Knowing that this is a strict preference and also wanting to avoid the unnecessary costs of implementing sanctions, the Respondent would never apply costly sanctions needlessly.Therefore, UCI Withdrawn (g, ∼ p, ∼ g) is the only outcome that is in equilibrium once Nature has revealed a poor UCI outcome in the range of g L I .A similar threshold exists if g I is sufficiently high.If g I is so favorable as to exceed the threshold defined as g H I , then the Initiator would continue to use UCI even if that meant it would surely suffer punishment from the Respondent.But once again, punishment is costly to the punisher and the Respondent would never suffer costs with no hope of the punishment being effective.Thus, the only outcome that can occur in equilibrium when g I falls above the threshold g H I is UCI Tolerated (g, ∼ p, g ′ ).
Lemma 1: R will never punish if Nature reveals that g I is in the ranges described by g L I or g H I .
Between these thresholds (g L I ≤ g I ≤ g H I ), the Initiator is satisfied with UCI outcomes enough to continue all else being equal, but not so satisfied that it would continue UCI if that meant it would suffer punishment from the Respondent.We define the outcomes of UCI between these thresholds as g M I .
Definition 3: Let w I + c ≤ g M I ≤ w I + c + x represent the range of g I at which I will choose ∼ g if R punishes, but g ′ if R does not punish in the previous move.
Here, the Respondent controls the outcome of the game and this decision is dependent upon how it is being affected by UCI, which is labeled g R .Call the threshold at which the Respondent would apply sanctions represent the threshold at which R is indifferent between punishing and not punishing I, given the condition Above this threshold, the effects of UCI on the Respondent are good enough that the Respondent would rather tolerate UCI than apply sanctions, meaning the only equilibrium is UCI Tolerated (g, ∼ p, g ′ ).Below this threshold, continued UCI would trigger sanctions and the only equilibrium is Successful Sanctions (g, p, ∼ g).At this point we understand what will happen once Nature reveals the results of UCI and this is illustrated in figure 2. However, the players can only arrive at this point in the game if the Initiator's beliefs are such that it will give Nature an opportunity to reveal g I and g R in the first place.This decision depends upon the Initiator's ex ante beliefs about how UCI might unfold.Let these beliefs about g I and g R be represented by θ I and θ R , respectively.
If the Initiator believes UCI will be worth the costs regardless of any punishment, (θ I ≥ g H I ), then I will always choose to initiate UCI and the outcome of the game will depend on the revealed values of g I and g R .Even if I is cautiously optimistic about how UCI will affect its own climate g L I ≤ θ I ≤ g H I , it may still use UCI if it believes that g R will be good enough for the Initiator to escape any punishment (θ R ≥ g * R ).Here again, these beliefs will cause the Initiator to test UCI and the ultimate outcome of the game will depend on Nature's determination of g I and g R .
Likewise, if the Initiator is pessimistic about the outcome of UCI (θ I ≤ g L I ), then it will never initiate.Even cautious optimism about its own outcome will not incentivize UCI if this cautious optimism (g L I ≤ θ I ≤ g H I ) is paired with pessimism for the . This is because this combination of beliefs will cause the Initiator to anticipate punishment that it is not willing to tolerate.With beliefs in these ranges, the only outcome in equilibrium is the Status Quo (∼g).
When we layer the beliefs that entice the Initiator to intervene in the climate alongside the effects of intervention as revealed by Nature, many equilibria emerge.These are illustrated in figure 3. We see that the Initiator will experiment with UCI only when its beliefs about the outcome are very optimistic (θ I ≥ g H I ) or when it is only cautiously optimistic for itself, but also optimistic for the . Next, we turn to the factors that determine these thresholds, and therefore, the likelihood of UCI.

Formal model implications
This formal model elucidates several conditions under which UCI may become more plausible, even when accounting for the possibility of punishment from another state.This section discusses further implications of the model and points to predictors of future UCI and several avenues for future research.Specifically, several conditions might increase the likelihood that a state pursues a strategy of UCI: Worse conditions in the present (low w I ): When states are less satisfied with their climates unaltered by climate intervention, the solution suggests that UCI is more likely to be seen as worth greater costs, punishments, and risks of failure.This is because deep dissatisfaction with the unaltered climate causes potential initiators to become more acceptant of even mildly successful interventions.Worse conditions in the present 'lower the bar' for what constitutes a worthwhile climate intervention, meaning that governments facing graver conditions in the present should be much more likely to turn to UCI in the near-term, all else being equal.If projections of the future climate are accurate, this result portends a world in which UCI is becoming more likely.
More confidence in UCI outcomes (high θ I , θ R ): Even if we assume that all states will have similar access to scientific information about the global effects of UCI, climatological factors will cause some states to be more confident of their own local outcomes than others.For example, some forms of UCI, such as SAI, may be associated with more predictable consequences at certain latitudes (Hueholt et al 2023, Labe et al 2023).Thus, a country's location on the surface of the Earth may be a key determinant of beliefs in climate intervention effects.Similarly, countries with more homogenous climates have fewer and less politically divisive outcomes that they are looking to optimize.Their programs could be much easier to tailor and may be much easier to predict.
Lower-or less sensitivity to-UCI costs (low c): Some states are going to be more sensitive to the financial and political costs of initiating UCI than others.Recent research on SAI suggests a globally effective program could be financed for less than $5 billion per year (Smith and Wagner 2018), and this is well within reach of many of the world's largest economies.These costs will vary by region.Recent scientific research also suggests that the efficiency of UCI methods like SAI vary greatly based on where on the planet these methods are used.Dai et al (2018), for example, found that SAI at mid-latitudes may have greater effect than SAI deployed in the southern hemisphere or near the equator.Non-financial costs, including political 'audience costs' imposed by unsupportive voters, could also deter governments from taking action (De Mesquita et al 2005).Countries experiencing more political stability and greater insulation from political opinion (non-democratic states and illiberal democracies) could therefore be more accepting of the risks inherent in experimental UCI, relative to budget-constrained governments that must soon face voters (Allen 2008).Together, this suggests the states facing the lowest costs for experimenting with UCI could be wealthy, northern, midlatitude states that face limited political competition.Deteriorating climate conditions may make a population more receptive to experimental climate interventions, thus reducing the political costs of a UCI trial.
Less sensitivity to punishment from other states (low x): Countries with substantial exposure to punishment from other states may be less likely to deploy UCI.This is because the more impactful a punishment is expected to be, the greater the results of UCI must be for a government to consider it worthwhile.Examples of countries that are more vulnerable to punishment, and therefore less likely to pursue UCI, include those that are highly dependent upon foreign imports of critical goods (Tostensen and Bull 2002), or, in the case of UCI methods like SAI, those that could be severely affected by restrictions on their use of neighboring states' airspace.Many types of climate intervention rely upon specific chemical compounds and/or advanced capabilities to build and launch high-altitude aircraft.Self-sufficient countries with sufficient domestic resources and capabilities are substantially less vulnerable to targeted sanctions (Lektzian and Patterson 2015).These vulnerabilities give potential respondents incredible leverage, and they therefore substantially influence an initiator's cost-benefit comparison (Bapat et al 2013).Countries that are less vulnerable to international airspace closures, such as coastal countries, or countries that export goods on which others are very dependent, such as energy products, are among the least sensitive to post-UCI punishment from other states.This may make them more likely initiators.
Lower probability of punishment (high s and low δ R ): From the perspective of a prospective respondent, some potential initiators are more costly to effectively punish than others (Pape 1997, Tostensen andBull 2002).Punishment is least costly to implement when the target of the punishment is relatively powerless and unable to retaliate.Conversely, large and powerful states have significant leverage in the international political economy and they can be both difficult and costly to coerce.The cost of effective punishment against these states can become too expensive to bear, even if another state's implementation of UCI degrades its climate.Some economists and international relations experts point to the high costs of effective sanctions to claim that sanctions are often ineffective if used (Pape 1997).Our model suggests fears that sanctions will not be effective can dissuade potential respondents from punishing other states in the first place (Smith 1995).
Our analysis also suggests that some states may be more willing to punish than others based on how much they discount the future (δ R ).UCI should be more likely when countries with the greatest leverage to punish a UCI initiator-major trading partners or geographic neighbors, perhaps-have significant problems in the present and therefore lack the luxury of prioritizing longer-term goals like climate actions.Governments facing pressing political problems are less likely to trade the short-term costs of imposing punishment for the long-term gains that punishment might produce (McLean and Whang 2014).In these cases, the short-term harm of sanctions enforcement may not be worth longer-term marginal changes in climate conditions.On the other hand, countries with trading partners and neighbors with more social stability and economic well-being may be more likely to place higher value on non-pressing longer-term policy goals, making them much more likely to implement costly punishment in the present so that they might realize longer-term benefits.

Implications
Proponents of economic globalization and multilateral global governance typically assume that increased interdependence decreases the likelihood of one state pursuing selfish interests at the cost of its political and economic partners (Keohane and Nye 2011).The model presented above casts some doubt on this generalization.If interdependence increases a potential initiator's exposure to punishment, but also makes punishment more costly for the respondent, then these changes could offset each other or even make UCI more likely.As the costs of punishment increase for a respondent, UCI must do more damage before the high cost of imposing punishment becomes worth the high cost of deterring UCI.This could embolden states seeking to begin climate intervention programs.Would other states jeopardize their own economies for a marginally negative change in the climate?Bold states considering UCI may bet that they would not.
Belief and knowledge about how the climate system may respond to UCI is an important component of our game theory model.Because of this, scientific research into climate intervention could impact the likelihood of UCI in multiple ways within our formal model.First, further improvements in scientific understanding of the consequences of SAI could affect the cost efficiency of UCI efforts.Second, research into the regional climate responses to UCI could affect the beliefs, as well as ultimate accuracy, of UCI efficacy.However, we note that a recent, systematic intercomparison of three Earth system models simulating SAI deployment found that model differences (e.g.representation of atmospheric circulation, aerosol microphysics) led to notable differences in the Earth system response to the same SAI forcing across climate models (Bednarz et al 2023, Visioni et al 2023).Thus, there is no guarantee that more scientific research will automatically lead to decreased uncertainty of the Earth system consequences of SAI.Third, if new research reveals that SAI benefits some parts of the globe at the expense of others, then this increases the chances that states would likely avoid altering the climate out of fear of punishment from an adversely affected state.This sort of asymmetric consequence of SAI might also create incentives for states in regions likely to be adversely affected by SAI to advocate for new international laws that strictly control UCI.This could then trigger more widespread and expensive penalties for any states that would otherwise initiate UCI for their own benefit.Multilateral sanctions of this kind simultaneously increase the costs to the initiating states while sharing the costs among a greater number of punishers.

Limitations
Formal models simplify complicated natural and political dynamics in an attempt to uncover the core drivers of strategic decision-making.They necessarily make simplifying assumptions about complex processes to gain analytical leverage.A useful model identifies key drivers of decisions, even if the mathematical representation of climatological outcomes and political decision-making neglect important nuances.
Crucially, this model assumes that states will be sensitive to the punishments imposed by others.The empirical evidence for this is mixed, though this deductive logic is a foundation for much of international relations theory on topics like coercion and deterrence.Writing long before the recent rounds of sanctions against Russia for its transgressions against its neighbors, Robert Pape argued, 'nationalism often makes states and societies willing to endure considerable punishment rather than abandon their national interests.States involved in coercive disputes often accept high costs, including civilian suffering, to achieve their objectives.Even in the weakest and most fractured states, external pressure is more likely to enhance the nationalist legitimacy of rulers than to undermine it ' (1997, pp. 106-107).Sanctions driven by rivals' UCI programs could be especially ineffective, given the difficulty that states will have drawing a direct line between specific-weather phenomena and SCI occurring outside of one's own national airspace (Keys et al 2022).
This model also assumes that states will both understand and agree about the outcomes of UCI, when in fact any post-UCI outcomes are very likely to be politicized.Voters are very likely to misperceive local effects of a major climate intervention, and anomalous events like major storms are very likely to steer public opinion and political action, even if these events deviate from clear general climate trends (Diffenbaugh et al 2023).This disconnect between the true and perceived effects of climate intervention introduces substantial uncertainty around potential reactions (Keys et al 2022).This means that initiators must consider that international punishment could occur, even if the scientific consensus is that UCI caused no harm.In the archetypal formal models, 'Nature' reveals outcomes that are as clear to all players as a poker dealer's draw.UCI outcomes are not so easily observed, and this means that reactions to UCI are likely to be much noisier and more uncertain than they are represented to be in a model.
Finally, this is a model of UCI initiation, but it is not a model of indefinite continuation, suspension, or international governance.In a multilateral world, reactions to UCI could include sanctions imposed by communities of respondents that can share the cost of punishment (NASEM 2021).Coalitions of states could join the initiator and effectively divide the world into blocks of climate intervention supporters and opponents.Successful climate intervention could create incentives for unabated carbon emissions, which could then transform the global economy and create insurmountable economic and political pressures to maintain climate intervention efforts.The possibilities are endless, but they are also so speculative that they are unlikely to affect a state's initial decision to begin UCI in a predictable way.This makes these topics critical for the future of climate intervention science and governance, but unimportant for modeling the drivers of a state's decision to initiate.
As others have so persuasively argued (Kravitz et al 2015, MacMartin et al 2022), a long-term SAI strategy is not a simple dichotomous choice to initiate or not, but it can instead be tailored, amended, expanded, or suspended in time.The wide menu of options would surely complicate decisions to initiate a program in the first place, perhaps by making initiation more likely.As knowledge of the effects of SAI specifications improves, it will become increasingly plausible that a state acting unilaterally could believe that it could optimize its own outcomes while minimizing adverse impacts on others.These decisions would unfold over longer time horizons, and a model of UCI initiation admittedly does not capture the many political and science-based decisions that could occur once an SAI program is active.
Ultimately, all formal models are inaccurate depictions of the decisions they represent, but some are useful.This model seeks to reduce UCI to the most basic concepts that might inform future decisions.As the literature develops, future models should explore variants where states can respond by joining the SAI effort or even trying to counteract it.Future models could add more variability and uncertainty by having Nature reveal a new randomized outcome for each period of gameplay.As SAI technology improves, the importance of the international regime governing the sovereignty of airspace may be less relevant.This could have profound impacts on who might initiate SAI and where it could occur.

Conclusions
We explore how UCI might unfold in the face of unrelenting climate change.Ultimately, the fundamental solution to addressing ongoing and future climate change is to reduce anthropogenic carbon emissions to net zero, or further (Pathak et al 2022).However, given the pace, scale, and stakes of global climate change, it is incumbent on the research community to understand the broader range of how society, united or otherwise, may respond.Using game theory, we show how a decision to engage in UCI is conditional on a chain of reciprocal interactions and perceptions.We anticipate future work could leverage our findings to shed light on how contemporary countries may play the game with one another.This could provide needed insight into the potential countries most likely to pursue UCI, and thus anticipatory capacity for international SCI governance.More immediately, this work could inform the composition of new simulations that complement global-scale deployments of SAI and imagine plausible unilateral actor scenarios confined only to their own and easily accessible parts of the Earth's atmosphere.

Figure 1 .
Figure 1.The unilateral climate intervention (UCI) game in the extensive form.Red payoffs are received by the Initiator, and blue payoffs are received by the Respondent.The game depicts an initial decision by the Initiator to try UCI or remain on the status quo path.Nature then reveals the outcomes of UCI for both states.The Respondent chooses whether to punish the Initiator, and the Initiator then decides to stop UCI or continue.The variables described in this section include climate for each state, both unaltered and altered by climate intervention, the cost of implementing a UCI program, the costs to suffer and deliver sanctions, and a standard future discount factor.

Figure 2 .
Figure 2. Possible outcomes following Nature's reveal of gI and gR.Punishment does not occur if the outcomes of UCI are so poor that the Initiator will stop without punishment, nor does it occur if the outcomes are so great that punishment would not be an adequate deterrent.The Respondent's decision to deter further UCI only matters for intermediate UCI outcomes, and this decision depends on how UCI affects the Respondent.

Figure 3 .
Figure 3.The Initiator's beliefs (θ1, θR) and UCI outcomes (g I , g R ). θ represents the Intiator's ex ante beliefs about the likely outcomes of UCI.The rows show the three relevant ranges of θI and the columns show the two relevant ranges of θR.In the upper-right portion of the matrix, the Initiator is optimistic enough to attempt UCI.In the lower-left, ex ante beliefs are too pessimistic for UCI initiation, even if its true outcome would be mutually beneficial.