Proliferation,preemption,and intervention in the nuclearization of second-tier states

Abstract

Traditional interpretations of politics among nuclear-weapons states—as epitomized by Schelling’s theory of deterrence through mutually-assured destruction—are less useful in today’s proliferation environment than they were during the Cold War’s superpower rivalry. As regionally-important states begin to pursue nuclear weapons, they do so in an environment that is shaped by the preferences and behaviors of the great powers. Using an elaboration on Powell’s bargaining model of conflict, this article shows that nuclear proliferation radically alters the future distribution of power, introducing a commitment problem vis-à-vis conventionally-stronger neighbors. This explains the occurrence of preemptive war in cases of attempted nuclearization, although the empirical paucity of such bargaining failures requires the shadow of great-power intervention in understanding the relations of second-tier states.

Keywords

bargaining model commitment problem extended deterrence nuclear proliferation second-tier states

1. Introduction

Joy was tangible on the streets of Islamabad in May 1998. Six times in the span of three days, the Pakistani government detonated nuclear weapons in the western Changai Hills. This feat of technological development, the creation of an ‘Islamic Bomb’, made Pakistan the ninth state to acquire nuclear weapons and overcame the military regime’s previous humiliation at the hands of its rival, India. Pakistan’s nuclear weapons program was decades in the making, and the 1998 test detonations were a sign and confirmation of the unstable south Asian state’s transformation from backwater to development, with the military and political power rightly held by a regional leader.¹

Nearly twenty-five years earlier, a different nuclear weapons program was abandoned in Egypt. Exasperated by 20 years of investment with few resulting technical or political gains, Anwar Sadat ended Cairo’s pursuit of nuclear weapons. The attempt to achieve parity with Israel, its regional rival, had backfired; by 1973 the United States affirmed the indispensability of Israel’s regional supremacy and assured Egypt that nuclear aspirations would only bring further rounds of violence to the Middle East.² Sadat found greater long-term diplomatic standing through embracing the non-proliferation regime instead, rather than continuing a militarized approach to the Arab–Israeli conflict.

At face value, these cases have many similarities. Both Pakistan and Egypt were mid-level, regionally important states aiming to increase their international standing. Both states faced rivals that had superior conventional military capabilities and a preexisting (although undeclared) nuclear option. However, Pakistan was successful at bringing a decades-long nuclear-weapons program to fruition, while Egypt was undermined by the lack of support for nuclearization from either the Americans or the Soviets. Existing research indicates that the pursuit of nuclear weapons, which greatly magnify military power at a relatively low cost, invite preemptive attack from those states that stand to be threatened.³ This paper aims to explain the differences in the international system, specifically the role of great-power preferences, that allow some states to successfully proliferate while others remain non-nuclear states by outside force. As nuclear proliferation becomes more of an issue among second-tier states, those that have regional, but not global importance and power projection, these states must make their decisions in the shadow of the United States and other great powers. Great powers can either protect members of the second tier, through alliances and support for joint interests, or they can harass smaller states to which they are opposed. Conversely, great powers can also be indifferent to the affairs of a faraway regional actor with whom it has no interests at stake.

The preferences of great powers were central to the first wave of international relations theory (cf. Waltz, 1979; Keohane, 1984). As research began to broaden its scope, looking at the nature of state-level interactions, great-power preferences became less prominent; however, the literature on intervention and extended deterrence both preserve the importance of great powers in determining the outcomes of international interactions. Powerful states can shield their clients from the consequences of threatening behavior, but do not similarly protect their enemies or the nonaligned. Enjoying the patronage of the United States, Russia, or China may have been sufficient for Israel, India, and North Korea (respectively) to successfully acquire a domestic nuclear weapons capability while avoiding a military strike in the interim from their adversaries. This paper contributes to the development of international relations theory by expanding the perspective of extended deterrence to the consequences of war prevention: when the threat of retaliation or preemption is deterred, what kinds of activities can a protected state pursue?

This paper is divided into four parts. Section 2 develops the theoretical background for the role of great-power intervention in protecting or deterring proliferation while placing it within the development of the international relations literature. It connects the substantive issue of nuclear proliferation to the theoretical construct of dynamic commitment, and shows why preemptive war should be expected when states pursue nuclear weapons. Section 3 presents a theory of international interactions in the shadow of intervention by a more-powerful state and introduces a bargaining model that formally explains the outcomes of these interactions in the context of nuclear proliferation. Section 4 elaborates on the empirical implications that can be drawn from the model. The paper concludes with an examination of two historical cases, which illustrate the plausibility of the theory’s predictions, before addressing the consequences for American non-proliferation strategy.

2. Literature

Levy (2008) notes several anecdotal cases in which states that pursue nuclear weapons are subject to preventive military strike by their neighbors. Contemporary attempts at nuclear proliferation by Iran and North Korea make the possibility of preventive military action extremely relevant to today’s policymakers.⁴ Nuclear weapons are inherently valuable for political (especially coercive) purposes, but among less-powerful states their military value directly affects the local balance of power, increasing newly nuclear states’ bargaining leverage vis-à-vis their neighbors. Anticipating this change, those states that stand to lose the most from nuclearization are incentivized to act during the period of time during which their advantage still exists.

The leverage provided by nuclear weapons comes from two complementary characteristics: the direct increase in military capabilities and first-strike incentives⁵ and, indirectly, the increased ability to impose unacceptable costs on the adversary ex ante bellum through coercion.⁶ Nuclear weapons are powerful instruments of war, yet in small numbers they are highly vulnerable. Lieber and Press (2006a) note that low levels of nuclear weapons are less survivable than are the larger arsenals associated with mutually assured destruction. If an adversary can easily disarm such a powerful weapon, there is a greater incentive to use that weapon offensively and earlier in an engagement. Below (2009) argues that a credibly survivable nuclear arsenal in the contemporary era requires roughly 1000 warheads, and that offensive incentives exist for states that possess fewer than that number.⁷

The second characteristic of nuclear weapons, the ‘power to hurt’, is more well-researched, as is their diplomatic–coercive application. Schelling notes that ‘[i]t is latent violence that can influence someone’s choice … The threat of pain tries to structure someone’s motives, while brute force tries to overcome his strength’ (Schelling, 1966, p. 3, emphasis in original). Nuclear weapons provide both the capability for latent (interpreted to be threatened countervalue) violence and brute force, although research has shifted focus between the two over time. Early research, such as that of Brodie (1946), was focused on the military applications of nuclear weapons, whereas their latent value became the primary focus soon afterwards.⁸ However, the counterforce and coercive applications of nuclear weapons are not substitutes for one another. Slantchev (2003) notes that increasing an adversary’s costs of conflict increases the range of mutually acceptable bargains, while increasing one’s available military capabilities shifts the location of that range.

As the Cold War progressed (especially with the Soviet development of nuclear weapons in 1949) the focus on nuclear weapons grew to encompass the deterrence framework exclusively.⁹ The number and force of nuclear weapons possessed by the great powers far outnumbered any military purpose, and the competitive escalation of the balance of terror became the principal effect of the nuclear rivalry (Lerner, 1962; Schelling, 1966; Huth, 1988). However, the continued proliferation of nuclear weapons to rising great powers and into the second-tier states made deterrence arguments less compelling. First, the numbers of nuclear weapons necessary for secure second-strike are lacking in newly nuclear states (Lieber and Press, 2006a,b, 2009). Second, the counterforce value of nuclear weapons is relatively much higher for smaller states, such as Israel (Quester, 1983), and attempted proliferators, such as Egypt (Levite, 2003; Rublee, 2006), than it is for states with large conventional militaries. As stated above, the offensive incentives associated with low levels of nuclear weapons and the cost-effectiveness of nuclear versus conventional balancing make their use a more rational option for these states than for the great powers. It is for this reason that contemporary nuclear coercion is the domain of the small states, while nuclear blackmail by the great powers is no longer seen as credible. Coercion by Israel, Pakistan, or North Korea is more credible than nuclear coercion by the United States or China, as the former group of states lack conventional alternatives with which to protect their national interests.

Dynamic commitment is an appropriate framework for analyzing this form of nuclear proliferation. In an anarchic environment where states are left to enforce their own agreements, the ability to commit to particular arrangements of coexistence is essential to stability (Fearon, 1995). In a static arrangement of power, where each party’s relative strength is commonly known, it is possible to establish cooperative equilibria based on the underlying distribution of power (Waltz, 1979; Axelrod and Keohane, 1985). Axelrod (1981, 2006) identifies several ways in which repeated interactions can lead to cooperative commitments even when incentives point toward non-cooperation at any given moment. However, this problem becomes more difficult in environments where states are becoming more or less powerful relative to one another. Organski (1958) first proposed the hypothesis that preemptive war may be a logical strategy for a strong state that sees the rising power of an adversary. Even though war is costly, preemption is preferable when an actor cares sufficiently about its declining future status that it is willing to pay upfront in order to maintain the status quo.¹⁰ Powell notes that ‘[c]omplete-information bargaining can break down … if the shift in the distribution of power is sufficiently large and rapid’ (Powell, 2006, p. 181). Thus, not all power transitions are likely to lead to preemptive war. Differential economic growth, the center of Organski’s theory, is too gradual a process to cause preemption (Powell, 1999, 2004). Rather, technological improvement in military capabilities should be examined when looking at dynamic commitment causes of bargaining failure.

Nuclear proliferation, by drastically increasing the military capabilities of a state (relative to a similar investment in conventional balancing) can succeed in shifting the mutually-acceptable bargaining range to a space that is entirely inconsistent with the prior distribution of power. As a result, anticipation of an adversary state’s nuclear weapons program should result in preemptive military strikes aimed at decapitating the means of power transition. While unaware of the general causal mechanisms behind bargaining failure, the nuclear proliferation literature has developed one of the more expansive collections of work on rational preventive warfare, especially those focusing on Israel’s 1981 attack against the Osirak nuclear reactor (cf. Feldman, 1982; Snyder, 1983; Feaver and Niou, 1996; Tamsett, 2004).

Fuhrmann and Kreps (2010) and Kreps and Fuhrmann (2011) address external factors of proliferation with the microfoundations of military prevention specifically in mind. They find that preventive military action against nuclear facilities is most likely when the perpetrator and target have divergent foreign policy views and when there is a history of militarized conflict within the dyad (Fuhrmann and Kreps, 2010). Furthermore, they find that the risk of international condemnation or direct retaliation from the target are not deterrents to preventive action when the target’s acquisition of nuclear weapons is deemed a serious threat to their national security. They do not directly address extradyadic actors, though they do note that military strikes put pressure on international suppliers and collaborators (among other consequences), reducing the matriel available to the target state (Kreps and Fuhrmann, 2011).

Given the incentives to militarily preempt the acquisition of nuclear weapons, why have there been so few instances of this type of bargaining failure? Extending the strategic framework to encompass multiple levels of bargaining changes the constraints that states face (Putnam, 1988). International actors that are not directly engaged in a dyadic bargaining process nonetheless have interests in the process’ outcome, and act (explicitly or implicitly) to influence its end state. This results in a different dynamic than in examining a dyadic interaction in isolation, one that has been most fully developed in the civil war literature (cf. Walter, 2002, 2009). Cetinyan argues that ‘[i]nefficient war due to a commitment problem might be averted, if the group that fears for its future were able to find an ally who, both groups believed, would intervene if the other group reneged on its promise to govern as agreed’ (Cetinyan, 2002, p. 671). This requires that third-party interveners be strong enough to enforce the dyad’s commitments.¹¹

Several recent quantitative studies of nuclear proliferation have probed the external political considerations that influence proliferation decisions. However, their approach to the power differential at play in contemporary cases is superficial. Singh and Way (2004), Jo and Gartzke (2007), and Fuhrmann (2009) all control for the presence of a great-power security guarantee. Based on Morrow’s (1993) interpretation of armament and alliances as substitutive, each of these articles hypothesizes that ‘[t]he allure of nuclear weapons as an avenue to security may be attenuated by a security guarantee in the form of a defense pact’ with a great power (Singh and Way, 2004, p. 869). However, these studies find mixed results, with the average effect of the security guarantee being an insignificant predictor of proliferation outcomes. This confounding result may be due to related methodological and theoretical reasons. By only controlling for cases in which a defense pact, the strongest formal signal of commitment, exists, these models ignore the de facto commitment expressed by states’ interest alignment. A formal commitment is only as valuable as it is credible: as a patron becomes more invested in its client’s well-being, it loses its ability to compel certain behaviors by threatening to end the alliance. Great power protection for nuclear aspirants (as well as for perpetrators of other illicit behaviors) can thus be induced through a state’s indispensability on other fronts.¹²

It is therefore misleading to think of an impartial arbiter as the paradigm for intervention. First, states intervene in disputes in which they are not direct participants only when it is in their own strategic interest to do so (Walt, 1985; Werner, 2000; Gent, 2007).¹³ Leeds (2003a) finds that great-power allies are less likely to honor alliance commitments because of reputational costs than are minor powers, lending support to the conclusion that self-interest is a necessary component of credible commitment. Second, Kydd (2003, 2005, 2006) finds that impartial mediation, when it is invoked, is less effective than intervention that favors one of the actors. States that mediate disputes with the sole intention of mitigating conflict or that ‘have no policy preferences at all over the issue in dispute’ are not seen as trustworthy, and their actions will be ignored (Kydd, 2003, p. 598). A threat of intervention by such an actor represents a static commitment problem, and is seen by other actors not to be credible.¹⁴

Intervention also creates a moral hazard that does not exist in isolated dyadic bargaining. Bapat (2010) notes that, because intervention bolsters the position of one actor vis-à-vis its adversary, that actor is likely to demand greater concessions. The end result of this is not only a further squeezing of the adversary state, but the entrapment of the intervener. Likewise, Smith (1996) finds that moral hazard extends to conflict initiation; when allied states are believed to be reliable, actors may seek out opportunities to provoke favorable intervention. Any intervention that has the possibility of meaningfully impacting the outcome of a bargaining process can also be exploited to create outcomes that are unfavorable to the intervener. How and when the external actor commits itself to certain behaviors (and how it communicates this commitment) becomes an integral part of the strategic calculations of the states that are directly involved in the bargaining process.

3. Theory

While commitment problems as a source of bargaining failure have been examined thoroughly within a dyadic framework, there is little analysis outside of the civil war literature¹⁵ that deals with the influence of external actors on these bargains. The interstate system allows for more powerful states to impress their will on less-powerful states, a dynamic that is central to understanding the practical limits of the dynamic commitment problem in leading to interstate bargaining failure. Furthermore, an understanding of dynamic commitment with a specific focus on the empirical question of nuclear proliferation allows a critical evaluation of the role that current great powers can play in shaping or controlling the expansion of nuclear weapons into the second tier of states and the effects that proliferation will have on international stability.

This section introduces a game-theoretic framework to analyze this problem. First, a two-stage dyadic bargaining model based on Powell’s (1999; 2006) bargaining model is introduced. The bargaining framework of the isolated dyad, so often used in international relations literature, is appropriate for bargaining among the ‘first tier’ of states: the great powers, which are sufficiently powerful that no other state exists that can meaningfully alter the bargaining relationship.¹⁶ Currently, the United States and China occupy the first tier; during the Cold War, the Soviet Union was also a first-tier state.¹⁷ Bargaining among these states is de facto isolated from external actors because no state has the capability necessary to effect change within their bargaining dynamics.

However, this is not the case with the majority of states, which exist in a system that is structured by the first-tier actors. Current nuclear aspirants (and their adversaries) must negotiate in the shadow of great-power intervention. Therefore, the bargaining model is expanded to include a strategic, ‘dictatorial’ actor who can (at a cost to itself) fix the distribution of benefits within the second-tier dyad in the event of bargaining failure. This model more accurately reflects the bargaining undertaken by second-tier states, which must account not only for their peers’ preferences and capabilities, but also for those of the system leaders. In comparing the dyadic and triadic games, it becomes clear that the threat of external intervention opens the possibility of extreme changes in the distribution of power without the occurrence of bargaining failure; this becomes more likely as the change is desired by the great power. However, a deviation of the great-power preference from the status quo ante is necessary for the other actors to alter their strategies from those of the isolated dyadic interaction.

3.1. Dyadic bargaining in isolation

3.1.1. Model introduction

The models in this paper draw heavily on the dyadic bargaining model developed by Powell (1999, 2006). The dyadic model (termed Γ₀, see Figure 1) is played between unitary rational actors, defined as the Defender (D) and the Challenger (C).¹⁸ The actors are engaged in a repeated interaction in which they must divide a set of benefits, normalized to the interval [0, 1], between them during each period. The actors have linearly increasing preference for the benefits and are either risk-neutral or risk-averse,¹⁹ characterized by ρ ∈ (0, 1]. At the start of the game, and for each period in which an agreement is not reached, the benefits are divided according to a status quo ante of (q, 1 − q) to C and D, respectively. Future gains are discounted by a commonly held discount factor δ ∈ (0, 1). The actors also have an exogenously predefined distribution of power (p, 1 − p), where p ≡ p₀ at the commencement of the game.²⁰

Figure 1.

First-round interaction for a two-player game (Γ₀).

The game is played in two periods. Prior to the initiation of the game, C decides whether or not to nuclearize. If C chooses to nuclearize, it sets in motion a process such that, in between t = 1 and t = 2, p ≡ p′ > p₀, unless the bargaining process is settled via the exit option. In addition, ’̣s costs associated with the inefficiency of war c_d increase to ${c^{'}}_{d} > c_{d}$ . If C does not nuclearize, p and c_d remain at their prior values for both periods. After this decision is made, the actors enter into the two-round bargaining game.

In each period t, D offers some x ∈ [0, 1]. C has the option of either accepting (A) or rejecting (R) x. If it accepts x, the distribution of benefits is redefined (x, 1 − x) at that period. If C accepts x at t = 1, that value becomes the status quo level q in the following round. If C rejects x, the distribution of benefits remains unchanged at the status quo level (q, 1 − q). After C makes its decision, both players receive their payoffs for the round, and they enter into the second round. After repeating the exchange for t = 2, the game ends.

However, both D and C have recourse to an exit option, war (W). By choosing this strategy, an actor permanently suspends the bargaining framework. The distribution of benefits is fixed at the ex post inefficient outcome (p_t − c_c, 1 − p_t − c_d) for all t moving forward.²¹

3.1.2. Solution

The solution to this game can be found through the subgame-perfect equilibrium (SGPE), a refinement of the Nash equilibrium that requires that actors’ strategies represent Nash equilibria at every subgame level of the overall game (Selten, 1975). Because the game is played in complete information, the process of backward induction allows for the identification of the SGPE (Gibbons, 1992). Separating at C’s initial decision over nuclearization, there are two parallel subgames that must be analyzed: one in which no nuclearization occurs, and one in which the process of nuclearization does occur.

Table 1.

Descriptions of parameters.

Parameter	Description
p_t = {p₀, p′}	Challenger’s share of power distribution
c_c, c_d	Costs of war to challenger and defender
q	Status quo distribution of benefits to challenger
x_t	Defender’s offer to challenger at time t
ρ_c, ρ_d	Level of risk-aversion for challenger and defender
δ	Discount factor
x_g	Great power’s ideal point*
c_g	Cost to great power of intervention*

Only used for Γ₁, the three-player model.

Table 2.

Move order for a two-player game (Γ₀).

t	Player	Move
0	Challenger	Chooses to nuclearize (N) or not nuclearize (¬ N)
1	Defender	Offers Challenger x ∈ [0, 1] or War* (W)
	Challenger	– If offered x, Accepts (A) or Rejects (R) or War* (W)
2	Defender	Offers Challenger x ∈ [0, 1] or War* (W)
	Challenger	– If offered x, Accepts (A) or Rejects (R) or War* (W)
		Game Ends

If either player chooses War (W), the game ends immediately.

Rational-choice literature has long held that the inefficient outcome of war should not occur in situations of complete information: the presence of such wars led to the initial evaluation of commitment problems (Fearon, 1995). Dynamic commitment problems exist as a consequence of changes in the distribution of power that are ‘sufficiently large and rapid’ (Powell, 2006, p. 181); however, an equivalent static commitment problem does not exist. Where the distribution of power is both stable and common knowledge, and where the distribution of benefits is sufficiently continuous (i.e. bargaining does not suffer from indivisibility problems), there should always exist a range of acceptable bargains and, given the decision rules posited above regarding offer-making, the range condenses to a unique equilibrium bargain.

Table 3.

Comparative statics for critical level of power $({p^{'}}_{c})$ in two-player game (Γ₀).

Variable	Symbol	$∂ ({p′}_{c})$
Challenger’s initial share of power distribution	p ₀	+
Challenger’s costs of war	c_c	+
Defender’s costs of war	c_d	+
Challenger’s risk-aversion	ρ_c	*
Defender’s risk-aversion	ρ_d	*
Discount factor	δ	–

See Figure 2.

Lemma 1. In an environment of static power (i.e. when p does not change), there exists an equilibrium bargain to the dyadic subgame at $x_{t}^{*} = {(p_{t} - c_{c})}^{1 / ρ_{c}}$ .

The proofs for this and other theorems are found in the appendix. Because D has the power to make the offer x, it is rational for the offer to make the maximum utility for D and, by complementarity, make C indifferent between accepting the offer and going to war.²² That is, D receives all of the gains from an efficient settlement of the bargaining process.

However, in situations of dynamic distribution of power, the option of preventive war becomes a viable option. C has every incentive to keep the bargaining process alive; at t = 2 the distribution of power shifts in its favor, and a non-null range of acceptable bargains is open as in the static case described above. However, prior to the power transition, D must calculate the expected benefits that it will lose to C as a result of C’s acquiring nuclear weapons (and the resulting change in the distribution of power). This expected loss is calculated relative to if D were to engage in preventive war, resulting in an ex post inefficient end state.²³ If the expected change in the distribution of power is sufficiently large, D’s expected loss from the power transition is greater than the costs of inefficiency, preventive war becomes personally rational for D. This holds even though the option is inefficient at the dyad level.

Theorem 2 (Preemption condition). In an environment of dynamic power, there does not exist an equilibrium bargain to the dyadic subgame when the change in the distribution of power between t = 1 and t = 2 exceeds ${p^{'}}_{c} - p_{0}$ , and there does exist an equilibrium bargain to the dyadic subgame at $x_{t}^{*} = {(p_{t} - c_{c})}^{1 / ρ_{c}}$ for each period when the change in the distribution of power does not exceed ${p^{'}}_{c} - p_{0}$ .

Once C has decided to pursue nuclear weapons, there are two possible end states. If the change in the distribution of power (represented by p′ − p₀) is sufficiently small, the change is absorbed by the bargaining process, and D is able to offer mutually acceptable levels of x in both rounds of the game, resulting in some shift of benefits away from D and to C’s advantage, that is nonetheless still preferable to war for both actors. However, if the expected change in power resulting from nuclearization is sufficiently large, D is unable to provide an offer at t = 2 that provides it with more long-term utility than would war under the terms of the initial power distribution. Faced with this prospective outcome, D’s rational strategy is to suspend the bargaining process upfront through preventive military action. Power transition theorists, such as Organski (1958) and Van Evera (1999), argue that a variety of factors, including differential economic growth, conventional armament, and even tactical advantages can be sufficient to result in bargaining failure. However, Fearon (1995) and Powell (2004, 2006) argue that future changes in power must be both extreme and sudden in order to frustrate the creation of a Pareto-superior negotiated settlement.

The formal model provides for a critical value ${p^{'}}_{c}$ , which determines, based on initial conditions, at which point the dynamic commitment problem exists for D. The critical value is defined as

{p^{'}}_{c} \equiv {[1 - {[\frac{(1 + δ) (1 - p_{0} - c_{d}) - {[1 - {(p_{0} - c_{c})}^{1 / ρ_{c}}]}^{ρ_{d}}}{δ}]}^{1 / ρ_{d}}]}^{ρ_{c}} + c_{c}

When changes in the distribution of power resulting from nuclearization exceed ${p^{'}}_{c} - p_{0}$ , the power transition induces bargaining failure; when the change is less than this value, the defender rationally accepts an unfavorable revision of the status quo while maintaining an efficient bargaining process. Figure 2 shows that, even under liberal grants of the cost of war and the actors’ risk-aversion, the required increase in power necessary to justify preemption is extraordinarily high.²⁴ Instead, a technological change that increases offensive incentives is necessary to reach the threshold for military action.

Figure 2.

Effect of starting distribution and risk-aversion on critical level of power.

This critical level is linearly dependent on the initial distribution of power for risk-neutral actors. The absolute level of change in the distribution of power is the same relative to the initial level of the distribution regardless of whether the challenger is more, less, or equally powerful relative to the defender in the status quo ante. Because this critical value is so high, states that exceed a certain level of initial power p₀ such that ${p^{'}}_{c} > 1$ will be theoretically unable to induce a dynamic commitment problem. In order to do so, their share of the distribution of power after the transition would require exceeding the total distribution. States that are conventionally powerful before they nuclearize are not likely to prompt bargaining failure vis-à-vis their weaker rivals; however, the dynamic commitment problem is a distinct possibility for challengers that are conventionally weaker than their rivals.

However, this linear relationship does not hold for risk-averse actors. Either the challenger or the defender acting in a risk-averse fashion changes the marginal effect of the initial distribution of power on the threshold level of the dynamic commitment problem. As the challenger’s risk-aversion increases, the marginal effect of p₀ on the critical change in the distribution of power increases, and the domain for which a dynamic commitment problem is possible becomes bounded. When the challenger is risk-averse, the dynamic commitment problem does not exist if the challenger is either too weak (p₀ < 0.1) or too strong (an increasing bound that is a function of ρ_c). As the defender becomes more risk-averse, in contrast, the bounds of p₀ do not change, but the critical value of ${p^{'}}_{c}$ increases at a curvilinear rate.²⁵ Figure 2 shows the threshold values of ${p^{'}}_{c}$ as a function of the initial distribution of power for various levels of challenger and defender risk-aversion.

The effect of p₀ on ${p^{'}}_{c}$ shows that the dynamic commitment problem is theoretically possible only for second-tier states. Because great powers, such as the first-generation proliferators, held a majority of the distribution of power vis-à-vis their rivals, it was impossible for any of these states to achieve the necessary leap forward in the distribution of power sufficient to prompt bargaining failure. The relative effect of nuclearization on their power was broadly accepted by less-powerful states, which did not have the ability to reverse the new status quo. However, states that are weaker than their adversaries initially can prompt bargaining failure through the anticipated expansion of their power that nuclearization provides.

The inefficiency costs of war for both C and D have a positive effect on the critical value of ${p^{'}}_{c}$ . This comes from the condition that D captures all of the gains from an efficient settlement, which is equal to c_c + c_d. As either of these increases, D has to suffer a greater loss of utility by engaging in preventive war vis-à-vis accepting the peaceful transition of power. It therefore requires that the expected loss resulting from the latter scenario increase respectively in order to make preemption personally rational.

A final effect is seen by the discount factor (δ) on the threshold. As to be expected, placing a lower value on future gains relative to present utility increases exponentially the critical expected change in the distribution of power necessary to induce the dynamic commitment problem. Where a state is sufficiently concerned with its present well-being relative to the future, it will not regard the consequences of future developments as pressing.²⁶ The effect of this is that a state that is sufficiently concerned with its utility in the present period will not intentionally suffer the inefficiencies of war, even at a favorable distribution of power, in order to avoid an unfavorable revision of the status quo in the future. Conversely, a defender that expects to have a long-term political relationship with the challenger is going to weight the post-transition environment more heavily than will a state with a short shadow of the future. This type of defender will therefore require less of an expected change from nuclearization to make bargaining failure the personally rational strategy.

The two subgames can be compared with one another directly, informing the challenger’s decision whether or not to pursue nuclear weapons in the first place. Initially, the challenger is indifferent between accepting the defender’s offer and going to war.²⁷ If nuclear weapons are not pursued, the static environment of the status quo ante remains undisturbed. Conversely, by pursuing nuclear weapons, one of two outcomes is possible. If the expected change in the distribution of power Δp is sufficiently high, this will provoke bargaining failure: the defender will preemptively attack the challenger before the power transition occurs. The challenger is indifferent between these two outcomes. However, if Δp is low, the defender accepts that nuclearization will occur, and continues the bargaining process while taking into account the new power that nuclear weapons bestow on the challenger. The resulting gain ${(p^{'} - c_{c})}^{1 / ρ_{c}} - {(p_{0} - c_{c})}^{1 / ρ_{c}}$ is transferred from the defender to the challenger. As a result of these possible outcomes, dyadic bargaining in isolation results in a consistent preference for pursuing nuclearization.

Theorem 3 (Nuclear preference in dyadic games). For Γ₀, C has a weak preference to nuclearize for all Δp.

Despite the possibility of a dynamic commitment problem, in the isolated dyadic interaction common to international relations literature, it is always part of the SGPE for the challenger to pursue nuclear weapons. The process of nuclearization is a calculated gamble by the challenger that it will be able to achieve this new military technology, and the added bargaining leverage that it entails, without inviting preemptive warfare to maintain the status quo ante. Success in achieving nuclear weapons is a function of the perceived effect of nuclearization (and the resulting threat) on the dyadic relationship. The result, as Debs and Monteiro (2010) show, is that nuclear proliferation is successful when its effect on the balance of power is relatively low, and either bargaining failure (prevention) or nuclear abstention occur when the effect of nuclearization is sufficiently high.

However, dyadic interaction is rarely in isolation from the remainder of the international system, and it is imprudent to ignore systemic impositions on the bargaining process. Great powers have their own interests over the stability of and distribution of power within the second tier of international powers. Even though these states may not overtly intervene in second-tier dyadic negotiations, their presence and the shadow of great-power intervention affect the strategic calculations of the challenger and defender, and may upset the equilibrium behavior of the dyadic interaction.

3.2. Bargaining in the shadow of a single intervener

3.2.1. Model introduction

The literature on civil wars has discussed at length the effects of intervention on dyadic negotiation (Werner, 2000; Cetinyan, 2002; Gent, 2007). When another actor has the ability to ‘dictatorially’ interfere (cf. von Glahn 1992, p. 171) externally in a dyadic bargaining process, by means of the application of outside reserves of power, the strategic logic of the initial dyad is altered. Actors must now consider not only how their strategies affect the behavior of their adversary, but also the intervener’s decision whether or not to involve itself in the dyadic bargain, and how intervention, if it occurs, affects the overall preferences of the initial actors.

Table 4.

Move order for a three-player game (Γ₁).

t	Player	Move
0	Challenger	Chooses to Nuclearize (N) or Not Nuclearize (¬ N)
1	Defender	Offers Challenger x ∈ [0, 1] or War^† (W)
	Challenger	– If offered x, Accepts (A) or Rejects (R) or War^† (W)
2	Defender	Offers Challenger x ∈ [0, 1] or War^† (W)
	Challenger	– If offered x, Accepts (A) or Rejects (R) or War^† (W)
		Game Ends
†	Great power	If either player chooses War (W), chooses to Intervene (I) or not to intervene (¬ I)*

If either player chooses War (W) and the great power does not intervene (¬ I), the game ends immediately.

The remainder of this paper examines several conditions under which the presence of a great-power intervener affects the likelihood of bargaining failure in the context of the dynamic commitment problem of nuclearization. Γ₁ (see Figure 3) introduces the player G, which has the ability to unilaterally correct for bargaining failures that may occur in Γ₀. G is assumed to be risk-neutral and has linear preferences over the distribution of the benefits between C and D. However, because G is not receiving the benefits itself, its preference is over the possible distributions between C and D relative to some exogenously defined ideal point x_g; G has lower utility for bargains that are settled at greater distances from x_g, and higher utility for bargains that are settled at shorter distances from the ideal point. This is represented by the negative absolute-value distance of the bargain, such that U_G(x) = −|x − x_g| (Hotelling, 1929).

Figure 3.

First-round interaction for three-player game (Γ₁).

Γ₁ differs from Γ₀ in that G has the ability to intervene in the dyadic bargain in the event of bargaining failure. When either C or D chooses the option of war, G may either intervene or not intervene. If G does not intervene, no change occurs to the outcome of Γ₀. If G does intervene, a dyadic bargain is enforced such that the division of benefits between C and D is set at (x_g, 1 − x_g) for that period. Because intervention is costly to G, it pays c_g > 0 whenever it intervenes.²⁸ G does not have the option of intervening if C and D agree to an outcome through the bargaining process.

3.2.2. Solution

The inclusion of G in the bargaining process serves as a failsafe in case of C and D’s failure to achieve an efficient outcome on their own. However, because intervention is costly, G will not always affect the strategic dynamic in the second-tier dyad. It will only do so when the benefit to be gained from intervention (i.e. its preferred outcome) outweighs the costs of achieving that outcome. Werner and Yuen (2005) note that the costs of intervention are related to the stability of the desired outcome. Where the great power’s preferred outcome is within the bargaining range (or can be within the bargaining range after a power transition), intervention can be limited in duration, fixing the commitment problem until the agreement becomes self-enforcing. However, if the outcome is non-self-enforcing, the intervention must be unlimited in scope and duration in order to maintain its stability (cf. also Bapat, 2010).

In the evaluation of a ‘hard case’ of intervention, G must maintain an indefinite commitment to the stability of the second-tier dyad. That is, G must be willing to pay the costs of intervention c_g indefinitely in order to achieve its ideal outcome, or chooses not to involve itself at all in the case of war. Thus, there exists a range of possible outcomes around the war outcome p₀ where it costs more for G to affect the outcome of bargaining failure than the utility it receives from moving to an ideal outcome from the natural one. Outside of this range, G is willing to remain committed to intervention for the full duration of the game.

Theorem 4 (Intervention condition). G credibly threatens to intervene in a degenerate bargaining scenario when x_g ∉ p₀ ± c_g.

Simply put, G can influence the strategic dynamics of the second-tier dyad when its ideal distribution of benefits differs from the initial distribution of power by at least as much as the cost expended in fixing the distribution of benefits. However, if the great power’s preferred outcome is eventually self-enforcing, an indefinite commitment is not necessary. Rather, G must only expend effort to fix the distribution of benefits until the power transition occurs. Because the great power only needs to pay immediate costs, rather than a discounted stream of costs into future periods, the range of G’s preferences that are credible threats of non-intervention is reduced.²⁹

Corollary 5. G credibly threatens to intervene in a degenerate bargaining scenario when $x_{g} \in [p_{0} + \frac{c_{g}}{1 + δ}, p_{0} + c_{g}]$ and when $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$ .

This can be interpreted as great-power patronage or protection for its protégé’s nuclear weapons program. Whereas the ‘hard case’ of intervention assumes the conditions under which G will interfere in the dyadic bargaining process based on its own interests and irrespective of the stability of such an outcome, the range of possible interventions is increased when the great power seeks, implicitly or explicitly, to improve the challenger’s standing relative to the defender. Being amenable in principle to a pro-challenger change in the distribution of power, G is able to extend the range of its influence toward more balanced outcomes. However, if the great power’s preferred outcome is not within the acceptable bargaining range after the power transition, G will only be able to intervene under the conditions of the ‘hard case’.

Corresponding with Theorem 4 and Corollary 5, great-power intervention is posited on G’s ideal point being sufficiently different from the initial distribution of power (and the anchoring point of initial bargaining outcomes). If the great power’s preference is sufficiently close to this distribution of power, G is willing to accept ‘natural’ outcomes from the dyadic bargaining process, without becoming directly involved. Great-power capabilities are not a sufficient factor by themselves to influence external outcomes—the shadow of intervention must also display a preference for change from the status quo in order to be relevant. Where this is not so, the dyadic interaction plays out as if it were in isolation.

Corollary 6. The inclusion of G does not affect the equilibrium path of play of Γ₁ away from that of Γ₀ if $x_{g} \in [p_{0} - c_{g}, p_{0} + \frac{c_{g}}{1 + δ})$ .

Where the difference between x_g and p₀ is sufficiently large, the interaction between C and D in the shadow of intervention is not identical to the isolated dyadic interaction. The credible threat of intervention creates a deterrent effect when G is sufficiently in favor of the challenger. However, when G’s preference is inverted, being sufficiently in favor of the defender, G’s presence creates a moral hazard.³⁰ In the isolated dyadic interaction, D chooses to suspend the bargaining process through war only as a result of the dynamic commitment problem; however, each period, when self-contained, has a range of acceptable bargains $x \in [{(p_{t} - c_{c})}^{1 / ρ_{c}}, 1 - {(1 - p_{t} - c_{d, t})}^{1 / ρ_{d}}]$ from which D may choose. By providing a credible threat of intervention when x_g ∉ p₀ ± c_g, D is presented with an alternative exit option from the bargaining process with a known and efficient value.³¹ When that utility is greater than the maximum that can be derived from the bargaining process, D provokes bargaining failure irrespective of the presence of a dynamic commitment problem or a nominally acceptable bargaining range.

Theorem 7 (Moral hazard). If x_g < p₀ − c_g and $x_{g} < {(p_{0} - c_{c})}^{1 / ρ_{c}}$ , D induces bargaining failure and provokes intervention regardless of C’s decision whether or not to nuclearize.

The scenario of moral hazard is not of direct interest to this research, but it is a necessary consequence of the shadow of great-power intervention. Whenever an actor has the ability to provide protection to one side in a bargaining process, it can induce riskier behavior on the part of the protected actor. When x_g is high, that protection allows C to strictly prefer a strategy of pursuing nuclear weapons. The challenger is protected from the possibility of preemptive warfare by the threat of favorable intervention. However, this effect works in both directions. When x_g is low, it is the defender who is protected both from the effects of its adversary’s power transition and from the bargaining process more generally. The same dynamic that allows the challenger to escape the dynamic commitment problem allows the defender to exploit the great power’s static commitment.

Examining the intervention conditions described above, great-power intervention is an off-equilibrium behavior. By credibly threatening to affect the dyadic bargaining process in C’s favor, G can successfully deter any attempt at preemption by D. When G can intervene, D receives greater utility from preserving the bargaining process and allowing C to successfully pursue nuclear weapons, and the additional bargaining leverage they provide, than by inducing G’s intervention. This holds regardless of the advantage Δp that C receives as a result of the nuclear power transition. In contrast, viewing the bargaining process in dyadic isolation shows that nuclearization is only successfully completed when $Δ p < {p^{'}}_{c} - p_{0}$ , when the challenger is already sufficiently powerful. Smaller states are able to successfully acquire nuclear weapons not because of their relative inutility, but because the shadow of great-power intervention deters any counteraction by the threatened defender.

Theorem 8 (Nuclearization condition). If x_g ≥ p₀ + c_g, C will successfully nuclearize.

Corollary 9. If $x_{g} \geq p_{0} + \frac{c_{g}}{1 + δ}$ and $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$ , C will successfully nuclearize.

As can be seen from Table 5, the inclusion of G shifts C’s preferences over the initial act of nuclearization. In Γ₀ C exhibits a weak preference for nuclearization under all conditions of the initial distribution of power (and a strict preference for values of $Δ p < {p^{'}}_{c} - p_{0}$ ). However, once the dictatorial intervener is allowed to alter the strategic considerations within the dyad, C exhibits this same preference only for the range x_g ≥ p₀ + c_g (or $x_{g} \geq p_{0} + \frac{c_{g}}{1 + δ}$ if $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$ ), where the great power is sufficiently biased in favor of the challenger vis-à-vis the status quo ante that it deters any form of preventive attack on the challenger’s nuclear program. This is the only condition under which nuclearization should be observed empirically.

Table 5.

Three-player nuclearization SGPE as a function of the great-power ideal point (x_g).

x_g ∈	Outcome
[p₀ + c_g, 1]	Challenger nuclearizes
	Challenger strictly prefers N to ¬N
$[p_{0} + \frac{c_{g}}{1 + δ}, p_{0} + c_{g})$	Challenger nuclearizes if $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$
	Bargaining failure if $x_{g} < {(p^{'} - c_{c})}^{1 / ρ_{c}}$
	Challenger weakly prefers N to ¬N
$[p_{0} - c_{g}, p_{0} + \frac{c_{g}}{1 + δ})$	Bargaining failure at t = 1
	Challenger is indifferent between N and ¬N
[0, p₀−c_g)	Moral hazard if $x_{g} < {(p_{0} - c_{c})}^{1 / ρ_{c}}$
	Challenger is indifferent between N and ¬N

For $Δ p < {p^{'}}_{c} - p_{0}$ , bargaining failure never occurs for x_g ∈ p₀ ± c_g, leaving the Challenger with a weak preference for N over ¬N in these domains.

For the subset of domains $x_{g} \in [p_{0} - c_{g}, p_{0} + \frac{c_{g}}{1 + δ}]$ , there is no meaningful intervention, as G prefers to allow bargaining failure fix the distribution of benefits rather than pay the cost itself of doing so. As a result, for values of x_g in this domain, the shadow of great-power intervention does not affect the bargaining process away from the dyadic game in isolation.

Finally, for sufficiently low values of x_g < p₀ − c_g, a moral hazard exists. Whereas sufficient bias toward the challenger deters any preemption, sufficient bias toward the defender induces this form of aggression. The apparent promise of support from the great power allows D to provoke bargaining failure at the earliest possible opportunity in order to move the distribution of benefits from $q = {(p_{0} - c_{c})}^{1 / ρ_{c}}$ to x_g.³² Again, this moral hazard exists irrespective of a future dynamic commitment problem, and so C’s decision to nuclearize is moot in determining the equilibrium state here.

4. Empirical implications

The dyadic and triadic models provide two different perspectives on the behavior of states in anticipation of a change to the distribution of power. While simplifications of reality, theoretical models provide powerful explanations of the causal logic behind behavior, both observed and unobserved, and provide expectations of behavior by rational states. Three implications are derived from the dyadic model Γ₀.

Implication 1 War should not occur between two states given a static distribution of power.

Implication 2 Preemptive war should occur in anticipation of an event that changes the distribution of power in a sufficiently large and rapid manner, but should not occur for sufficiently small or gradual changes in the distribution of power.

Implication 3 States are naturally incentivized to pursue nuclear weapons under all possible changes to the distribution of power.

The first two implications are consistent with the existent literature on bargaining theory and commitment problems (cf. Debs and Monteiro, 2010), while Implication 3 is drawn from a comparative analysis of subgames varying the challenger’s decision to pursue nuclear weapons. If bargaining were indeed conducted in dyadic isolation, all states that have the ability to pursue nuclear weapons should take that strategic choice. However, very few states have attempted to pursue nuclear weapons, and even fewer have succeeded in acquiring them.

The refinement described in Γ₁ conditions dyadic behavior on the shadow of great-power intervention in the bargaining process. This splits the challenger’s incentives over nuclearization. When great-power preferences are sufficiently biased in favor of the challenger, nuclearization can be successful, and the challenger’s strict preference for nuclear weapons is carried over from the dyadic into the triadic bargaining process. However, where that bias does not exist, second-tier states are indifferent over the possible outcomes of the bargaining process. This results in the following implications:

Implication 4 Nuclearization will not occur if the great power’s preferred distribution of benefits is sufficiently similar to the status quo.

Implication 5 Nuclearization is less likely to occur when the costs of intervention are high or when the great power’s shadow of the future is sufficiently short.

Implication 6 A state is more likely to procure nuclear weapons without incident when the great power is sufficiently biased in its favor.

Nuclearization, especially successful acquisition of nuclear weapons, should be seen most often among the second tier of states where the challenger is under the patronage of a great power that is relatively unencumbered in its dealings with the international community. As the great power becomes more constrained through higher costs of intervention, the range of protégé states whose nuclear weapons programs can remain under its protection decreases. However, extreme bias in favor of a challenger should be sufficient to shield its domestic pursuit of nuclear weapons from external challenge.

This finding runs contrary to the conventional wisdom that alignment with a much stronger state should exert a deterrent effect on nuclearization. While armament and alliances are substitutes for each other, the patron’s ability to deter its client’s domestic armament is limited by the alignment of the patron’s and client’s interests. When the patronage is de facto (based on natural alignment between the patron and client) rather than de iure (based on a formal alliance), the patron cannot credibly threaten to separate itself from the client, removing a key means of compellence (cf. Leeds, 2003b). In addition, increased client capabilities reduces the expectation of direct support from the patron. This serves as an incentive for the patron to acquiesce to domestic armament by its clients. Having induced the protection necessary to succeed in nuclearization, the client state is less likely to demur from increasing its own capabilities.

Strategic interactions rarely take place in isolation from external factors. This paper explains how the dynamic commitment problem resulting from the pursuit of nuclear weapons can be ‘resolved’ through the shadow of great-power intervention. Extended deterrence prevents retaliation against a protégé, providing sufficient protection to bring a nuclear-weapons program to completion. However, in the absence of this protection, attempts at nuclearization are met by direct action when the perceived costs of tolerating proliferation are too high. The absence of the dynamic commitment problem in a large number of second-tier attempts at nuclearization is a function of this great-power patronage, while the few cases that resulted in military action reveal attempts at undermining the nonproliferation regime without the support of a larger state.

5. Historical illustrations

While there are few historical cases of middle-power nuclearization that have come to fruition, they provide concrete support for overcoming the commitment problem by way of great-power deterrence. Israel, India, Pakistan, South Africa, and North Korea have all developed nuclear weapons capacities, in part dependent on the protective shadow of great-power intervention. However, 17 other states (cf. Levite, 2003) have had serious attempts at nuclear-weapons or dual-use research, but have not attempted to cross the threshold of nuclearization because of a lack of great-power support. The cases of Pakistan and Egypt help to illustrate the two deterrent effects of the shadow of great-power intervention on the commitment problem of nuclearization.

5.1. Pakistan: a case of preemption deterred

Pakistan’s interest in a nuclear program began shortly after its independence, with the 1954 US-sponsored ‘Atoms for Peace’ program. While the program (and Pakistan’s newly-formed Atomic Energy Commission) did have a legitimate interest in augmenting the country’s insufficient conventional energy sector, the government remained ambiguous on its official policy vis-à-vis weaponization. While the military government initially vetoed the pursuit of a domestic nuclear-weapons program, concerns about India (already the conventionally superior military force in the region) led to a deterrence orientation by the late 1960s (Kapur, 1987). Constrained by immediate military concerns in Kashmir, Pakistan did not make nuclearization a national priority until after the Smiling Buddha nuclear test in 1974 (Marwah, 1981; Ahmed, 1999): ‘After the Indian explosion, however, the nascent Pakistani weapons program had to move forward according to the realist view: facing a recently hostile neighbor with both nuclear weapons and conventional military superiority, it was inevitable that the government in Islamabad would seek to produce a nuclear weapon as quickly as possible’ (Sagan, 1997, p. 59).

The first signs of Pakistan’s move toward weaponization came in 1977, as the United States and IAEA became aware of Pakistani reprocessing and enrichment activities.³³ By 1983, Pakistan was sufficiently close to a weapons capability, which it probably acquired shortly thereafter. (Pakistan maintained a position of strategic ambiguity about its nuclear capability until it conducted test explosions in 1998, so it is uncertain when exactly it acquired its nuclear weapons capability.) This was achieved largely with the assistance of China, itself a nuclear weapons state and, like Pakistan, an adversary of India.³⁴ Since then, Pakistan has developed an arsenal of approximately 60 nuclear weapons with regional range, which is believed to be a larger arsenal than India’s at approximately 50 weapons.³⁵

Why then did India, which had achieved its first nuclear capacity at least 10 years prior, not preempt the Pakistani nuclear program? According to Kapur (1987), India had sufficient conventional capabilities to suppress the Pakistani military, as it had in earlier conflicts.³⁶ However, such engagements were costly, even as the Indian military consolidated its regional superiority.³⁷ Furthermore, India could not overcome the Chinese, who had aligned with Pakistan against India since the Sino-Soviet split in the 1960s. The 1962 Sino-Indian border war helped to confirm Pakistan’s acknowledgment of China’s aversion to the pro-Russian regime in Delhi.³⁸ Over the following 20 years, China provided both technical and material assistance to the Pakistani nuclear program, consisting of transfers of highly enriched uranium and enrichment infrastructure, in the attempt to tilt the balance of power against India (Ahmed, 1999).³⁹ China’s position clearly indicated that Pakistani nuclearization would be beneficial for the regional alliance as well as for the furtherance of ‘revolutionary change that would work to the benefit of the Third World.’⁴⁰ While Pakistan could not entice China to collaborate on the 1965 or 1971 Indo-Pakistani conflicts, the possibility of regional destabilization meant that the Chinese provided a latent deterrent while Pakistan developed its own nuclear capability (Arquilla, 1997). Despite India’s dyadic superiority, it was unable to overcome Pakistan’s alliance with the superior Chinese forces.

Factions within the Indian political establishment, while recognizing Pakistan as an enduring rival, were most concerned about the expansionist role of China in South Asia (Hedrick, 1999; Karnard, 2002; Bajpai, 2007). China and India had been involved in a rivalry for regional dominance since 1949, as the only two large states in south and south-east Asia. The Indo-Pakistani conflict, derived from the 1947 partition, was initially unrelated to the Sino-Indian rivalry; however, the two became linked in the context of regional balancing: China’s assistance to and cover for the Pakistani nuclear program is, in hindsight, a clear sign of that intent. Given the intimate connection between the Pakistani nuclear program and China’s patronage, India could not disentangle its two rivals (Perkovich, 1999). To risk preemptive action against the nascent Pakistani program would entail bringing the Sino-Pakistani relationship to the conflict’s front (Garver, 2001). In addition, there was no guarantee that preemptive action would succeed in disabling Pakistan’s program. Perkovich notes that ‘[t]he least risky strategy was to bide time, avoid provocations, pursue diplomacy and keep the nuclear “powder” dry while downplaying either side’s explicit interest in nuclear weaponry’ (1999, p. 254). As a result, India largely conceded to Pakistan the development of a nuclear arsenal. The one time that India did threaten action (the 1987 exercise named BRASSTACKS, the largest military maneuver since World War II), it was too late to effect change. Through both diplomatic channels and public media, Pakistan acknowledged its nuclear weapons capability, a shocking response to the Indian strategy of regional intimidation (Ahmed, 1999).⁴¹ This news brought BRASSTACKS to an abrupt conclusion: the window of opportunity had passed India by.

The Pakistani case provides illustration that pressure by a great power can deter attempts to preempt middle-power nuclear programs. Whereas Pakistan had been militarily inferior to India since the partition of the former British colony, China had a clear interest in expanding Pakistan’s power vis-à-vis their common enemy. This interest manifested itself not only in the assistance provided to the Pakistani nuclear program, but in the protection that China gave to its client, via the threat of intervention in an Indo-Pakistani conflict. Unable to resolve the realignment by use of overwhelming force, India was forced to accept a degree of increased Pakistani influence in the region. Although it had been dominant in the first 40 years of their dyadic relationship, since 1987 India has been forced into a scenario that more closely resembles the mutual nuclear deterrence of the great powers.⁴²

5.2. Egypt: a case of nuclearization deterred

Egypt also developed its interest in nuclear energy through its participation in the ‘Atoms for Peace’ program during the 1950s, toward the beginning of the Nasser regime. However, military applications were not Egypt’s principal concern until 1960, when the regime became aware of Israel’s Dimona reactor and the military direction of its neighbor and rival’s nuclear program (Quester, 1983; Rublee, 2006). The Egyptian nuclear weapons program was therefore a direct challenge to that of the Israelis, who had bested the combined Arab armies during the 1948 war. The defeat of the Egyptians, who were for centuries the political center of the Muslim world, moved the regime toward a militarized perspective on nuclear energy in an attempt to reclaim the mantle of political importance (Gerges, 1995; Levite, 2003; Rublee, 2006).

However, the Egyptian nuclear weapons program was plagued by early failures. By the 1967 war, Cairo was no closer to developing a weapon than it was seven years earlier (Rublee, 2006). Egypt’s major patron, the Soviet Union, was only willing to supply a 2 MW research reactor, and no other state would engage Cairo on nuclear research or technology sales until the 1990s, years after Egypt ratified the Nonproliferation Treaty (NPT) (Gregory, 1995).⁴³ The Israelis, on the other hand, had a sophisticated domestic nuclear program, including technological control of the entire nuclear fuel cycle, and were believed to have already created a number of nuclear weapons by this point.⁴⁴ Furthermore, the United States came to ally itself with Israel only in the aftermath of the 1967 war (Ben-Zvi, 2007). As the CENTO initiative to contain Soviet influence in the Middle East fell through, the United States came to focus more on its alliances with Israel and Iran, while fearing the revolutionary pan-Arabism of the Nasser regime.

The traditional framework of mutual deterrence would indicate that Egypt would further expand its nuclear weapons program, given its inability to defeat the Israelis conventionally. However, American involvement in the Middle East, biased as it was in the context of Cold War containment, led the Sadat regime to renounce its militarized nuclear program (Siler, 1992; Levite, 2003). While the United States was biased toward the Israelis, it had hoped to resolve the regional conflict so as to turn its attention toward the Soviet Union. Bar-Joseph (1982) argues that the Soviet Union was similarly not interested in escalating the Arab–Israeli conflict toward nuclear war.⁴⁵ ‘Sadat knew that any alliance with the United States would require complete abandonment of the nuclear program. The expectations and diplomacy of global powers can make a difference, if the state in question values the alliance more than the nuclear weapons program’ (Rublee, 2006, p. 561). Through the use of selective incentives, both positive (a security guarantee vis-à-vis Israel) and negative (threats to withhold economic assistance, as well as technological embargoes), the United States was able to deter Egypt from the escalatory path of nuclearization (Levite, 2003).

The 1973 war was the final blow to Egypt’s designs for a nuclear weapons program. During this war, the United States came to the support of Israel despite the threat of Soviet escalation and an Arab oil embargo. This show of resolve to keep Israel at the top of the Middle Eastern hierarchy led Sadat to view the nuclear program as a one-time bargaining chip rather than as an instrument for increasing Egypt’s share of the dyadic distribution of power (Rublee, 2006). The lengths to which the United States risked its own interests to support Israel made it clear that the (highly difficult) process of nuclearization would not result in concessions from Israel, but in further violence.⁴⁶ After losses in 1967 and 1973, as well as the ‘war of attrition’ in 1970, the cumulative costs of war and the observance of direct U.S. assistance to Israel led Egypt to abandon this method of technological growth. Rublee notes:

‘Sadat decided that it was in Egypt’s best interest to give up the nuclear program and used it as a tool to bargain with the United States after the 1973 war with Israel. Sadat promised to ratify the NPT and give up Egypt’s nuclear ambition for good if the United States would aid Egypt—a deal that Washington accepted. From 1974 to the present, Egypt has remained true to its promise, embracing the nuclear nonproliferation regime and energetically participating in it, hoping to force Israeli movement on the nuclear issue.’ (Rublee, 2006, p. 556)

While unable to reverse the distribution of power entirely, Sadat was able to garner enough American support through this diplomacy to regain the Sinai peninsula from Israel in 1979, and to cement Egypt’s position as the leader of the Arab negotiating bloc vis-à-vis Israel for a generation.

The theory of great-power intervention provides support for why Egypt ended its nuclear weapons program after 13 years. As the United States moved from Egyptian ally during the 1950s to an aloof observer in the 1960s to the advocate of Egypt’s regional enemy from 1967 onwards, the opportunities to revise the distribution of power away from Israel began to falter. Part of this was due to direct interdiction efforts (cf. Gregory, 1995); however, the political intent to nuclearize was clearly present until the United States had signaled its willingness to absorb costs to maintain a pro-Israel status quo. Having suffered severe costs during each attempted revision, Egypt was rationally incentivized to avoid provocation and accept the distribution of power as it was, while exploiting available opportunities to marginally alter the distribution of benefits.

6. Conclusion

The technological shock of nuclear proliferation drastically changes the distribution of power among second-tier states, with consequences for the division of benefits among them in the international system. This paper has shown that, when treated in dyadic isolation, the appropriate response to second-tier nuclearization is preemptive military action, which preserves the status quo ante. However, military action is not a dominant strategy when a proliferating state is under the protective shadow of a great power. In cases where a great power is biased in favor of the potential proliferator, the threat of intervention may be sufficient to overcome the dynamic commitment problem. States facing a relative decline opt for the ‘lesser of two evils’ resulting from their adversary’s acquiring nuclear weapons.

Policymakers should be particularly attentive to the role of great-power preferences in incentivizing nuclear proliferation. As potential proliferators are more closely aligned with a great-power patron, they ensconce themselves in their patron’s rationally extended deterrence, becoming more insulated from the consequences of the dynamic commitment problem. Conversely, as great powers are more neutral in their approach to second-tier interactions, endorsing a realpolitik distribution of benefits in line with the underlying distribution of military capabilities, the benefits of nuclearization to a potential proliferator become less apparent. This same effect occurs as the great power becomes less capable of providing protection to its clients (through increased costs of intervention). While focusing nonproliferation efforts directly at the state pursuing nuclear weapons has been a common-sense approach for the last 40 years, this paper shows that the behavior of proliferators’ adversaries and protectors are intimately related to the success of any nuclearization effort, and that a more comprehensive and inclusive approach to nonproliferation is needed to address the causes of nuclearization success.

Several characteristics of this relationship remain to be elaborated on. The model presented in this paper accounts for a single great power with defined interests that are commonly known. However, there are several states capable of intervening in the second tier that comprise current and future cases of nuclear proliferation. These states will not always have similar interests, and the aggregation of multiple opposing interveners may lead to an escalation of regional conflicts (as was the case during the Cold War) or mutual deterrence, which would allow second-tier interactions to play out as if in isolation. This latter case is possible even when there is not a conflict of interest, as Gent (2007) describes. In addition, information problems resulting from this aggregation may lead to other forms of bargaining failure.⁴⁷ Even with a single great power, how its preferences on multiple issue areas are translated over a second-tier dyad is an unresolved question.

This paper provides a first attempt to bring the bargaining dynamic of nuclear proliferation out of the dyadic context. The world in which superpowers negotiate in isolation over the structure of the international system is gone; however, the great powers play an important role in structuring the interactions of the second tier, where the proliferation battle is being played out and will continue in the future. Multilevel strategic interactions are not well-examined in contemporary research, but will become more necessary as the number and types of important actors continues to multiply in the international system.

Footnotes

Appendix: Proofs

Proof of Lemma 1. The utility to C of taking its various strategy options is defined by the present value of the stream of period utilities. In a two-period game, the strategy at t = 1 takes into account both the full value of that period’s payoff, and the value of the payoff in t = 2 discounted by the factor δ. The possible responses lead to C’s utility functions as defined per period:

\begin{array}{r} U_{C} (War) & = & p_{t} - c_{c} \\ U_{C} (Accept x) & = & x^{ρ_{c}} \\ U_{C} (Reject x) & = & q^{ρ_{c}} \end{array}

Assume that U_C(q) = U_C(War) (i.e. that the bargain is initially in equilibrium). This leaves C with the following strategy, based on utility maximization:

s_{C} = {\begin{array}{l} Accept & if x \geq {(p_{t} - c_{c})}^{1 / ρ_{c}} \\ Reject & if x < {(p_{t} - c_{c})}^{1 / ρ_{c}} and x \geq q \\ War & if x < {(p_{t} - c_{c})}^{1 / ρ_{c}} and x < q \end{array}

D’s utility functions are defined similarly to C’s:

\begin{array}{r} U_{D} (War) & = & 1 - p_{t} - c_{d, t} \\ U_{D} (x | Accept) & = & {(1 - x)}^{ρ_{d}} \\ U_{D} (x | Reject) & = & {(1 - q)}^{ρ_{d}} \end{array}

Irrespective of the status quo ante q, D can eliminate C’s option of war by offering $x \geq {(p_{t} - c_{c})}^{1 / ρ_{c}}$ . This is personally rational for D, because a Pareto-efficient outcome results in all gains going to D. Therefore, D’s offer is defined by

\begin{array}{l} s_{D} & = & \underset{x}{arg max} 1 - x | x \in [{(p_{t} - c_{c})}^{1 / ρ_{c}}, 1 - {(1 - p_{t} - c_{d, t})}^{1 / ρ_{d}}] \\ = & {(p_{t} - c_{c})}^{1 / ρ_{c}} \end{array}

D’s range of possible acceptable offers x is bounded by the threshold to war for each state. Because D has the power of initiative, it offers the minimum value x which maximizes its utility ${(1 - x)}^{ρ_{d}}$ . This is equal to the minimum value that C (weakly) prefers to its exit option. Conversely, D’s strategy would be war if there did not exist any x that satisfies the above argument (i.e. the set is null).

At t = 2, D is the only one who stands to lose from an unraveled bargaining process. D therefore offers $x_{2} = {(p - c_{c})}^{1 / ρ_{c}}$ , which is the minimum value of x₂ that C will accept. (Given the static distribution of power, p refers to the same value at both t = 1 and t = 2.) Thus, in equilibrium, at t = 2 C is indifferent between the outcome resulting from war and the bargain proposed by D. Retrogressing to t = 1, C is indifferent between the expected utility of its future payoffs: suspending the bargaining process or continuing it each results in an expected utility of (p − c_c). Therefore, C’s action at t = 1 is based on the offer x₁ according to the same decision rule s_C described above. Again, D maximizes its utility by offering $x_{1} = {(p - c_{c})}^{1 / ρ_{c}}$ , which C accepts, thus ensuring the continuation of the bargaining process (and the accrual of bargaining gains to D).

Proof of Theorem 2. Given a change in p occurring at t = 2, each actor’s strategy in t = 1 will be conditioned on the present value of the full stream of payoffs. Given p_t₌₂ = p′, the equilibrium behavior after the power transition is

\begin{array}{l} s_{C}^{2} & = & {\begin{matrix} Accept & if x \geq {(p^{'} - c_{c})}^{1 / ρ_{c}} \\ War & if x < {(p^{'} - c_{c})}^{1 / ρ_{c}} \end{matrix} \\ s_{D}^{2} & = & arg max 1 - x | x \in [{(p^{'} - c_{c})}^{1 / ρ_{c}}, 1 - {(1 - p^{'} - {c^{'}}_{d})}^{1 / ρ_{d}}] \\ = & {(p^{'} - c_{c})}^{1 / ρ_{c}} \end{array}

Thus, if the bargaining continues after the change in the distribution of power, there exists an equilibrium bargain for t = 2 at $x_{2} = {(p^{'} - c_{c})}^{1 / ρ_{c}}$ , which C accepts (cf. Lemma 1). Continuing backward to t = 1, C’s utility functions are defined as such:

\begin{array}{r} U_{C} (Accept x_{1}, Accept x_{2}) & = & x_{1}^{ρ_{c}} + δ x_{2}^{ρ_{c}} \\ U_{C} (Reject x_{1}, Accept x_{2}) & = & q^{ρ_{c}} + δ x_{2}^{ρ_{c}} \\ U_{C} (War, Accept x_{2}) & = & p_{0} - c_{c} + δ (p_{0} - c_{c}) \end{array}

Assuming that $q = {(p_{0} - c_{c})}^{1 / ρ_{c}}$ at t = 1 (i.e. that the bargain is initially in equilibrium), C excludes the option of war by being indifferent in t = 1 between rejecting x₁ and war, and preferring the former outcome in t = 2 to that of war. Therefore, C’s strategy in t = 1 is defined by

s_{C}^{1} = {\begin{matrix} Accept & if x \geq {(p_{0} - c_{c})}^{1 / ρ_{c}} \\ Reject & if x < {(p_{0} - c_{c})}^{1 / ρ_{c}} \end{matrix}

There exists an equilibrium bargain at t = 1 if and only if there exists a value x₁ that D prefers to war. Anticipating that x₂ exists in equilibrium, D’s utility functions at t = 1 are defined as follows:

\begin{matrix} U_{D} (x_{1}, x_{2} | s_{C}) & = & {(1 - x_{1})}^{ρ_{d}} + δ {(1 - x_{2})}^{ρ_{d}} \\ U_{D} (War, x_{2} | s_{C}) & = & 1 - p_{0} - c_{d} + δ (1 - p_{0} - c_{d}) \end{matrix}

A dynamic commitment problem exists when D’s utility to war, which is ex post inefficient, results in a greater personal utility to D. Conversely, an equilibrium bargain exists when D’s utility to war is less than the utility of some bargain x₁ for t = 1. Given $x_{2} = {(p^{'} - c_{c})}^{1 / ρ_{c}}$ , the dynamic commitment problem does not exist for any x₁ such that

{(1 - x_{1})}^{ρ_{d}} + δ {(1 - {(p^{'} - c_{c})}^{1 / ρ_{c}})}^{ρ_{d}} \geq (1 - p_{0} - c_{d}) (1 + δ)

Simplifying for x₁, there is an equilibrium bargain when

x_{1} \leq 1 - {[(1 + δ) (1 - p_{0} - c_{d}) - δ {(1 - {(p^{'} - c_{c})}^{1 / ρ_{c}})}^{ρ_{d}}]}^{1 / ρ_{d}}

x₁ is effectively bounded at the minimum by $q = {(p_{0} - c_{c})}^{1 / ρ_{c}}$ .⁴⁸ As this threshold level of x₁ is a function of both the expected future distribution of power p′ and the current distribution of power p₀. Solving for the unknown value p′ shows that, for a given level of initial conditions p₀, c_d, c_c, ρ_d, ρ_c, and δ, there exists an equilibrium bargain in the shadow of shifting power when

p^{'} < {[1 - {[\frac{(1 + δ) (1 - p_{0} - c_{d}) - {[1 - {(p_{0} - c_{c})}^{1 / ρ_{c}}]}^{ρ_{d}}}{δ}]}^{1 / ρ_{d}}]}^{ρ_{c}} + c_{c}

Let ${p^{'}}_{c}$ be defined as the minimum level of ${p^{'}}_{c}$ for which an equilibrium bargain no longer exists.

For all changes in the distribution of power $Δ p < {p^{'}}_{c} - p_{0}$ , D may offer $x_{1} = {(p_{0} - c_{c})}^{1 / ρ_{c}}$ , which is accepted by, C and the bargaining process remains efficient. However, for all $Δ p \geq {p^{'}}_{c} - p_{0}$ there is no x₁ that D can offer that results in a utility stream greater than that of war.

Proof of Theorem 3. In the subgame of Γ₀ that begins with C’s choice ¬N, C has an expected utility of (p₀ − c_c)(1 + δ) (cf. Lemma 1). In the subgame that begins with C’s choice of N, C has an expected utility of (p₀ − c_c)(1 + δ) when $Δ p \geq {p^{'}}_{c} - p_{0}$ (which results in immediate bargaining failure) or (p₀−c_c) +δ (p′ − c_c) when $Δ p < {p^{'}}_{c} - p_{0}$ (where Δp does not trigger a dynamic commitment problem). Given these outcomes, C is indifferent between N and ¬N for $Δ p \geq {p^{'}}_{c} - p_{0}$ , and strictly prefers N to ¬N for $Δ p < {p^{'}}_{c} - p_{0}$ , indicating a weak preference for nuclearization for all Δp.

Proof of Theorem 4 and Corollary 5. In the event of bargaining failure, G intervenes if the benefits in achieved utility outweigh the costs of intervention. G’s utility to war at t = 1 is defined as follows:

U_{G} (War) = - | p_{0} - x_{g} | (1 + δ)

The utility to intervention is instead a function of whether intervention is self-enforcing or not.⁴⁹

Case 1: x_g is self-enforcing

x_g is defined as self-enforcing when intervention at t = 1 does not require a subsequent intervention at t = 2 in order to maintain this outcome. x_g must therefore be within the range of acceptable bargains after the power transition, namely $x_{g} \in [{(p^{'} - c_{c})}^{1 / ρ_{c}}, 1 - {(1 - p^{'} - {c^{'}}_{d})}^{1 / ρ_{d}}]$ . The utility to G of intervention in this case is therefore

U_{G} (Intervention) = - c_{g} + δ (0) = - c_{g}

G prefers to intervene when it receives a greater utility from doing so, or when

- c_{g} > - | p_{0} - x_{g} | (1 + δ)

This is true for $x_{g} \notin p_{0} \pm \frac{c_{g}}{1 + δ}$ . Because $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$ as a result of the self-enforcing requirement, G does not intervene when its preference is below the status quo distribution of power. Rather, G intervenes at t = 1 when $x_{g} \geq p_{0} + \frac{c_{g}}{1 + δ}$ and $x_{g} \geq {(p^{'} - c_{c})}^{1 / ρ_{c}}$ .

Case 2: x_g is not self-enforcing

x_g is not self-enforcing when intervention at t = 1 does not set $q_{2} = x_{g} \in [{(p^{'} - c_{c})}^{1 / ρ_{c}}, 1 - {(1 - p^{'} - {c^{'}}_{d})}^{1 / ρ_{d}}]$ , and G must intervene at both t = 1 and t = 2 in response to bargaining failure. In this case, the utility to G of intervention is

U_{G} (Intervention) = - c_{g} + δ (- c_{g}) = - c_{g} (1 + δ)

G prefers to intervene when it receives a greater utility from doing so, or when

- c_{g} (1 + δ) > - | p_{0} - x_{g} | (1 + δ)

This is true for x_g ∉ p₀ ± c_g. This condition is independent of p′ and, for x_g > p₀ + c_g, is subsumed within the domain $x_{g} > p_{0} + \frac{c_{g}}{1 + δ}$ for Case 1, although without that case’s other constraint that $x_{g} > {(p^{'} - c_{c})}^{1 / ρ_{c}}$ .

Conversely, for x_g < p₀ − c_g, G will also be incentivized to intervene in a scenario of bargaining failure at t = 1. When $x_{g} > {(p_{0} - c_{c})}^{1 / ρ_{c}}$ as well, this creates a situation of moral hazard, whereby D is incentivized to provoke bargaining failure independently of the dynamic commitment problem.

Proof of Corollary 6. Per Theorem 4 and Corollary 5, G intervenes in bargaining failure at t = 1 for x_g ∉ p₀ ± c_g, or for $x_{g} > p_{0} + \frac{c_{g}}{1 + δ}$ when $x_{g} > {(p^{'} - c_{c})}^{1 / ρ_{c}}$ as well. For $x_{g} \in p_{0} \pm \frac{c_{g}}{1 + δ}$ , G does not receive greater utility from intervening (even in a self-enforcing scenario) than it does for allowing the bargaining process to play out as in the dyadic scenario. Per Corollary 5, $x_{g} \in [p_{0} - c_{g}, p_{0} - \frac{c_{g}}{1 + δ})$ does not satisfy the self-enforcing condition; therefore, G likewise does not have an incentive to intervene in the dyadic bargaining process.

Proof of Theorem 7. This follows directly from Theorem 4 for x_g < p₀−c_g and $x_{g} < {(p_{0} - c_{c})}^{1 / ρ_{c}}$ , cf. Case 2 above.

Proof of Theorem 8 and Corollary 9. Per Theorem 4, for x_g > p₀ + c_g, D prefers not to induce bargaining failure at t = 1 due to the shadow of G’s threatened intervention. As a result, C strictly prefers N to ¬N. Per Corollary 5, this follows for $x_{g} \in [p_{0} + \frac{c_{g}}{1 + δ}, p_{0} + c_{g})$ when $x_{g} > {(p^{'} - c_{c})}^{1 / ρ_{c}}$ . Because G does not need to sustain intervention in both periods when x_g is a self-enforcing equilibrium at t = 2, the threat of a single-period intervention is sufficient to provide C with a strict preference for N over ¬N. (When $x_{g} < {(p^{'} - c_{c})}^{1 / ρ_{c}}$ , bargaining failure occurs at t = 1, and C is indifferent between N and ¬N.)

Acknowledgements

The author would like to thank Navin Bapat, Anna Bassi, Mark Crescenzi, Stephen Gent, Andrew Pennock, and two anonymous reviewers for their helpful comments. The analysis in this article does not reflect the official position or policy of the Department of State or of any other agency of the U.S. Government. Any errors remain the responsibility of the author.

Notes

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