Principal and One Dyad

I derive the agent's utility from a model of the utility of nuclear weapons in a local arms race. States in general are motivated by a desire to influence other states, and the asymmetric possession of nuclear weapons provides them with such influence. Two agents are engaged in an arms race modeled as a prisoner's dilemma, with temptation payoff z − c, sucker payoff −z, cooperation payoff normalized to 0 and suboptimal payoff −c. The index of rivalry between the two countries is z with z an integer drawn in the [1,N] segment. At this point, z can be interpreted as an agent's compliance cost (this is the right that the principal covets). The cost for an agent of building nuclear weapons is c with c > 0.

Both z and c are common knowledge. I assume common knowledge because asymmetric information would detract from the primary interest of this study, which is the relative importance of bilateralism, multilateralism, and exclusion in the NPT regime.

The principal values disarming by one agent at V > 0 and nondisarming at 0. The principal confronts each agent separately with a contract that (1) offers payment a in exchange for an agreement to disarm, (2) threatens sanction d in the case of no agreement, and (3) threatens sanction s in the case where an agreement is reached but the agent is thought to have armed nevertheless. This three-incentive structure closely mirrors the text of the NPT, which, as was shown earlier, combines one carrot and two sticks.

The principal incurs a per-agent cost ɛs for executing sanction s and a per-agent cost ρd for executing sanction d with ɛ and ρ > 0. I ignore transaction costs for now, for they are of no relevance to this preliminary game.

I also assume that promises and threats are credible ex ante. Credibility is the result of a costly signaling game or a reputation game that is not modeled here because it is unnecessarily complex. Leaving the credibility-generating mechanism out of the game, however, is bound to lead to absurd results with respect to incentives that do not fall on the equilibrium path, such as sanctions. For instance, the principal could threaten a hellish punishment and extract compliance at no cost because she would be released from having to deliver on the sanction threat. Unless the cost of sanctioning figures on the equilibrium path, any sanction value goes. To circumvent this problem, I assume that the mere threat of sanctioning is costly. The principal incurs a per-agent cost σs for threatening s and a per-agent cost δd for threatening d with σ and δ > 0. The two threat costs capture, in much-reduced form, the ex ante costs that a principal must sink prior to uttering a threat in order to establish a reputation, often through the initial imposition of high-cost sanctions.Footnote ¹⁹

Compliance with treaty obligations is not directly observable by the principal. The probability that an agent who cheats is not caught by the principal is q. For convenience, AppendixTable A1 lists the notation used in the model.

The principal moves first, then the agents sequentially decide to reject or accept the offer. At no loss to generality, I assume that agent 1 moves first, agent 2 second. If neither accepts, the game ends. If one rejects and the other accepts, the former is sanctioned and the other chooses whether to comply and be rewarded, or cheat and be rewarded with q probability and punished with probability 1 − q. If both accept, then they simultaneously choose between complying and cheating (they do not observe each other's choice) and are either rewarded or punished accordingly. The game tree is drawn in Figure 1.

FIGURE 1.

Game tree for the principal-and-one-dyad game

A strategy for the principal specifies the (a,d,s) regime she proposes. A strategy for agent 1 is the mapping (a,d,s) → {A,R} and (a,d,s) × {A} × {A,R} → {C,S} specifying for every possible regime whether to accept or reject and, after accepting and for every possible decision of agent 2, whether to comply or shirk. Similarly, a strategy for agent 2 is the mapping (a,d,s) × {A,R} → {A,R} and (a,d,s) × {A,R} × {A} → {C,S}. The solution concept is the subgame perfect Nash equilibrium.

The principal has a clear goal—nonproliferation—which her control of the agenda enables her to achieve by following a simple strategy: offer a regime that leads the agents successively to accept the offer and comply with the obligation of disarming. To enable such result, the principal's choice of design must satisfy a certain number of constraints. A first set of constraints, called “participation constraints,” insures that each agent prefers “accept” and “comply” to “reject.” Depending on what the other agent is doing, there are two participation constraints for each agent. A first participation constraint insures that agent i prefers “accept” and “comply” to “reject” given that agent j rejects, with i,j = 1,2. Formally, −z + a ≥ −c − d. In other words, the agent's payoff for acceptance and compliance, which is equal to sucker payoff −z plus transfer a, must be greater than or equal to the agent's payoff for rejecting the contract, which is equal to the suboptimal payoff −c plus the harm caused by the sanction for not participating −d.

A second participation constraint insures the same result given that j accepts and complies. Formally, a ≥ z − c − d, with, on the left side, the cooperation payoff (normalized to zero) plus transfer a, and, on the right side, the temptation payoff z − c plus the sanction payoff for not participating −d. This second constraint is mathematically identical to the first constraint.

In addition to insuring that agents participate, the principal must also insure that they comply. Two constraints, called “incentive constraints,” must be satisfied to insure that result. A first incentive constraint requires that i prefers “accept” and “comply” to “accept” and “shirk” given that j rejects. Formally, −z + a ≥ −c + qa − (1 − q)s. The left side is the same as above. The right side features the suboptimal payoff −c, the transfer a, which the cheating agent receives with q probability, and sanction payoff −s, which he receives 1 − q of the time. A second incentive constraint insures the same result given that j accepts and complies. It is mathematically identical to the first incentive constraint and need not be repeated.

Three additional constraints are required to prevent carrots from changing into sticks and sticks into carrots: a,d, and s ≥ 0.

Solving the game is tantamount to solving a constrained maximization problem—program P ¹—in which the principal chooses the mix of incentives a,d, and s so as to maximize her utility for disarming the two agents subject to the five aforementioned constraints:

The principal's payoff U _P is, for each agent, the gain for disarming V minus the paid transfer a, further diminished by the aggregate cost of threatening sanctions δd + σs.

The solution to the problem yields a unique equilibrium for each configuration of parameters V,δ,σ,z,c, and q. More precisely, depending on the relative marginal costs of the incentives that are featured on the equilibrium path, respectively unity for rewarding, δ for threatening to sanction nonparticipation, and σ for threatening to sanction cheating, the solution features either a reward-only regime, a regime with sanctions only, a regime with only one sanction, or any mix thereof. Since the determination of the incentive structure of a particular regime—the particular mix of sticks and carrots—is not the primary goal of this article, I only solve the game for the incentive structure that most closely conforms to the reality of the nuclear proliferation regime: a mixed-incentive structure or a,d, and s > 0. The solution to the principal-and-one-dyad game is stated in the following proposition.

This result is proven in the Appendix. Note that the equilibrium is calculated for a and s as a function of d. This is because the mixed-incentive equilibrium is underspecified and can only be determined for two choice variables as a function of the third.Footnote ²⁰ I chose to make d the determinant for reasons that will become apparent in the empirical section. Also note that both the reward and the two sanctions are present in the equilibrium because the reward has the same marginal cost as the two sanctions added together. This knife-edge condition does not necessarily mean that the mixed incentive equilibrium is a zero-probability event. More likely, it represents the unresolved nature of the debate on the relative efficiency of carrots and sticks, a debate that is fueled by the fact that different interest groups often have opposite stakes in this debate.

The result in proposition (1) exhibits both intuitive and counterintuitive causal connections. On the intuitive side, first, both transfer a and sanction against cheater s increase with the cost of compliance z, suggesting that countries that find it hard to part with nuclear weapons invite a higher price to join in and a steeper sanction to comply. Equally intuitive is that both incentives decrease in c, the opportunity cost of disarming. Also, a rise in nonparticipation sanction d logically commands a lower transfer a to participants; splurging on the sticks allows the principal to save on the carrot—carrot and sticks are interchangeable.

Less intuitive is that a rise in the sanction against nonparticipation, d, commands a higher sanction against cheating, s. This is because a rise in d brings into the regime members with higher compliance costs, who would not have joined otherwise, and therefore are harder to deter from cheating. Expanding membership to tough types without further repressing cheating is cause for cheating. This conclusion is in line with the link between “deep cooperation” and the need for enforcement underlined by Downs, Rocke, and BarsoomFootnote ²¹ as well as the simultaneous widening of European integration and deepening of its judicial system.Footnote ²²

Principal and “N” Dyads

I now expand the model to a large number of dyads. I make the simplifying assumption that each country is part of only one dyad. The assumption captures the main idea that arms races are local, in the sense that Brazil worries about Argentina getting the bomb a lot more than North Korea or Iran. Note, though, that the assumption leads one to ignore arms races that are not strictly dyadic but involve three or more countries—Chile also worries about Brazil and Argentina getting the bomb.

Dyads differ with respect to the rivalry index, z. For the sake of simplicity, I assume that the dyads are distributed discretely on z; they are numbered according to the intensity of rivalry z _k with k varying from 1 to N, such that z ₁ = 1, z ₂ = 2,…, z _N = N. Hereon, z _k may be interpreted as an agent's marginal cost of compliance: it is equal to the marginal value that each agent attributes to a prize equally valued at 1.

The incentive structure of the regime again is of the mixed type.Footnote ²³

The principal's choice variables are twofold: whether to exclude or include, and, in the case of inclusion, whether to do so only by means of a multilateral treaty or also with bilateral instruments. The two types of instruments differ in two respects. First, a multilateral treaty provides all signatories with the same contract irrespective of their compliance costs. It is analogous to the law of one price in market economics. In contrast, a bilateral instrument allows the principal to offer each agent his own compliance cost. The bilateral approach is equivalent to market segmentation practiced by monopolists.

Second, the transaction costs for the multilateral approach are lower than for the bilateral approach. Transaction costs is a basket category, initially coined by economists to explain why market relations, understood as a contract between two independent individuals, might fail to maximize these individuals' joint utility.Footnote ²⁴ Here, I adopt a restrictive definition of transaction cost as the contractual costs incurred in the process of making a deal. Aggregate transaction costs are lower for the multilateral approach to regime building than for the bilateral approach because there are scale economies in bargaining and dealmaking.Footnote ²⁵ I model this feature by assuming that any deal, bilateral or multilateral, costs constant T to process, with T positive.

From these two differences, it follows that the principal matches instrument with agent's compliance cost: (1) the multilateral treaty is calibrated to the low and intermediate marginal-cost agents, (2) bilateral instruments are directed to intermediate cost agents, and (3) exclusion targets high cost agents. To see this, first imagine a situation with no transaction cost. The principal only uses bilateral contracts. This is easily seen in Figure 2A, in which I map the cost to the principal on the vertical axis as a function of the agent's compliance cost z on the horizontal axis, with integer v > 1 a point on the z axis. To keep the graph two-dimensional, it is assumed that the only incentive that is available to the principal is the transfer a(z); s(z) = d(z) = 0. The cost of wooing countries with compliance cost less or equal than v by means of a multilateral contract is equal to the va(v) rectangle, because the multilateral approach forces the principal to pay the transfer it pays to v to all agents left of v. In contrast, by means of bilateral contracts alone, this same cost would be equal to ∑₁^va(z), the triangle situated below the curve, which is only half the size of the rectangle. The triangle above the curve is a surplus that I refer to as the “agent surplus” in direct analogy with the “producer surplus” of market economics.Footnote ²⁶

FIGURE 2A.

Impact of transactions costs

With a transaction cost T significantly different from 0, however, the v bilateral contracts could be costlier than a multilateral contract. This case is represented in Figure 2B, where the cost of the multilateral contract is the same as before plus the transaction cost incurred once (va(v) + T), while the cost of the bilateral contracts is the former triangle augmented with the transaction cost incurred v times (∑₁^va(z) + vT).

FIGURE 2B.

Impact of transaction costs

Finally, there is a higher value of v past which the bilateral approach becomes the less costly of the two again. Indeed, it is easy to verify that as v increases, so does the relative size of the c b a(v) triangle relative to the cde triangle. Therefore, from the principal's perspective, the presence of transaction costs makes the one-treaty approach more efficient than the bilateral approach for low-compliance-cost countries, but less efficient for high-compliance-cost countries.

Although I have assumed so far that every country is included, this need not be so. The principal would like to exclude countries with excessively high compliance costs. She gains nothing from an agent's nonparticipation, she may actually lose something if she sanctions them; and yet she is nevertheless better off excluding than including these countries in the regime.

Combining these different insights yields the solution template drawn in Figure 3 (also drawn under the assumption that s(z) = d(z) = 0). On the left-hand side of the graph, in the (1,x] segment, the agent's cost is sufficiently low that it makes sense to seek nonproliferation by offering a reward and by doing so through a single generic contract, minimizing transaction costs but providing a surplus to all the agents to the left of x. In the middle part of the graph, in the (x,y] interval, each agent's compliance cost is too high in relation to the fixed transaction cost for overlooking the surplus. Rather than offering a beefier multilateral contract, the principal tops off the existing multilateral contract with bilateral contracts customized to each member of the interval. Finally, there is a third group of agents on the right-hand side of the graph, the (y,N] segment, with costs of compliance that are so high that it is not in the interest of the principal to even try to elicit their compliance. To put it succinctly, the regime should obey the following generic condition:

FIGURE 3.

Solution template

The analogy with consumer economics assumes that the incentive is a reward. What if, instead, the principal merely threatens to sanction noncompliance? The analogy still works provided that one is ready to think of sanctions as negative prices. For instance, Santa Lucia, a country better known for its beaches than its desire to pursue nuclear weapons, would comply with the proliferation ban even if she were given negative price −s or, to put it more intuitively, even if she were asked to pay s in addition to complying. The fact that she is not asked anything besides compliance means that she saves s. Generally speaking, positive incentives set the agent's reservation value to 0, whereas negative incentives set the reservation value below 0.

Solving the N-dyad game allows for the principal to choose cutpoints x and y that maximize her aggregate utility while simultaneously satisfying the constraints necessary to have y dyads take the mixed-incentive contract and comply. Formally, it means for the principal to solve program

Function g(z) is the principal's payoff for extending a mixed contract to a country with war intensity z. It is constructed by substituting the equilibrium values of proposition (1) into the principal's utility function previously defined in P ¹. The first two terms of the principal's utility function U _P are the principal's net gain for the multilateral treaty with the first x dyads: she gives to each of the x dyads of that group the same treatment as to the dyad with the highest marginal cost of compliance in that group, z = x, and pays only one transaction cost. The summation term is the principal's net gain for the y − x dyads with which she signs 2(y − x) bilateral treaties with as many transaction costs.Footnote ²⁷ The last term is the cost to the principal of excluding N − y dyads from the regime.

The problem affords different types of solutions depending on the values taken by x and y. I do not solve for all of them, but focus instead on the one that corresponds to the NPT regime—the mixed instrument regime (not to be confused with the mixed incentive structure also present in the NPT regime), featuring a multilateral treaty, numerous bilateral agreements, and the exclusion of a handful of countries. This is the case for which 1 < x < y < N. That equilibrium is stated in proposition (2) and proven in the Appendix.

Clause (1) summarizes the multilateral instrument, clause (2), the multilateral together with the bilateral instruments, and clause (3), the conditions of exclusion. Incentives are higher for agents who receive bilateral instruments. Note also that the equilibrium obtains for a specific family of parametric configurations, which one may characterize as intermediate values of transaction cost T expressed as a function of the other parameters. A T that is too small takes the wind out of the multilateral instrument, whereas a very large T prices out all types of instruments.

Rivalry and Affordability

I test the rivalry and affordability conjectures by correlating the principal's decision whether or not to include a country in the regime with that country's security characteristics and wealth. A nonparticipant being a nonsignatory, the dependent variable is npt ratification, coded 1 for ratification and 0 for nonratification.

Ratification is a unidirectional decision: once made, it is typically not, with one exception, taken back. Moreover, countries that ratified did it over a period of thirty-plus years (see Figure 4), during which many countries' security position changed. I use the technique of event history modeling that allows one to focus on the spell of time before ratification occurs and study the respective impact of cross-national and time-varying covariates.Footnote ³¹

FIGURE 4.

Number of ratifications and total number of countries

A first set of independent variables seek to capture the rivalry index (z). A key implication of the local arms race is that countries that feel threatened by their neighbors should be less eager to give up their right to acquire nuclear weapons. I assume that the sense of insecurity reflects the history of conflict. I alternatively use two measures of a country's history of conflict. A first measure hostility is the sum of the Correlates of War (COW) indices of hostility levels with contiguous states averaged over the prior twenty years.Footnote ³² A second measure, enduring rivalry, is participation in an enduring rivalry because most militarized disputes occur in the context of enduring rivalries.Footnote ³³

A country's sense of insecurity may also reflect the regime type of its neighbors. Building on the democracy and war literature, I venture that being in the neighborhood of democracies provides a country with a greater sense of security than if it were surrounded with autocracies. The variable democratic neighbors is a weighted average of the democracy score of a country's neighbors. I used national capabilities as weight to select out information on a country's neighbors that are smaller than the country and unlikely to represent a military threat.Footnote ³⁴

The modeling of the local arms race as a prisoner's dilemma suggests that the worst outcome is for one side to give up nuclear weapons unilaterally, for then the other side has an advantage in not doing so. This suggests that a country would not join the NPT regime unilaterally, but in coordination with its neighbors. One observes instances of this logic in Western Europe and in the Southern tip of Africa. I created the variable neighbor's ratification, which for a given country, identifies all its contiguous countries, determines whether or not they have ratified the NPT, and weighs that score with their relative power.Footnote ³⁵

The presence of a security threat may not lead a country to acquire nuclear weapons if the threat is offset by a security guarantee from a nuclear power (variable a). Security guarantees figure as one of the most effective bargaining tools that the United States and the Soviet Union used in their respective bilateral efforts to stop proliferation. I build the variable superpower's defense guarantee, which identifies all the countries toward which the United States or the Soviet Union/Russia had a formal defensive obligation during the year of observation.Footnote ³⁶ I am aware that many of the guarantees that are included in the dataset were not granted bilaterally but through a collective security treaty—NATO for example. I treat them as bilateral instruments nevertheless because the model does not recognize a regional level different from the bilateral and multilateral levels. There is also the fact that NATO—the most “collectivist” of the regional arrangements—is not a symmetric alliance: with the notable exception of the American superpower, no single member country is indispensable to the survival of NATO, not even Britain or France.

Not quite a security guarantee, but a source of U.S. leverage nevertheless, is u.s. aid per capita, the total amount of economic and military aid provided by this country and calculated as a proportion of the population of the receiving country.Footnote ³⁷

The second independent variable is the affordability of a nuclear weapon program (−c), proxied by the wealth and size of the country: The larger and wealthier a country, the easier and more desirable the acquisition of nuclear weapons. I use total population to proxy for size and gdf per capita to proxy for level of development.Footnote ³⁸

I round off the test with several control variables representing possible alternative accounts of a government's decision to ratify the NPT. A first control variable is peer pressure. Constructivists argue that, as more countries uphold the regime, the regime gains in authority and nonparticipants are hard-pressed to join. An easy measure of peer pressure is the cumulative number of members. I call this variable total ratification.

A second control variable is the end of the Cold War, which, according to realists, took the wind out of global regimes. I create the dichotomous variable 1991–2002, coded “1” during the corresponding years and “0” otherwise.

Moreover, Singh and WayFootnote ³⁹ found an occasional role for regime type, the idea that a democracy is less likely to pursue nuclear arms and thus more likely to join the nonproliferation regime.Footnote ⁴⁰

I estimate four Cox proportional hazards models on various combinations of independent variables. The proportional model is preferable to a parametric model in the absence of a particular theory about the way time affects the causal impact.Footnote ⁴¹ The universe is all sovereign countries in a given year, with the exclusion of the five nuclear powers recognized in the NPT. The results are presented in Table 1.

TABLE 1.

Cox models of NPT ratification

Notes:

Coefficients are estimates for Cox proportional hazards model; robust standard errors, adjusted for clustering by country, are used to calculate the p values for two-sided tests. GDP = gross domestic product.

*** p < .01;

** p < .05;

* p < .10.

The results for the baseline model, listed in column (1), seem weak at first sight—none of the security risk and bilateral guarantee variables are statistically significant. A closer examination of the data identifies as the cause for the unexpected result the Rio Pact countries: being a member of the Rio Pact makes a country less likely to sign and ratify the NPT than not being a member. Controlling for the Rio Pact in the other columns brings the security and guarantee variables in line with the present argument. There is one apparent exception to this generalization, the variable u.s. aid per capita, which in models 1, 2, and 3 is wrongly signed. Once again, a closer look at the data reveals that this result is not robust, but instead the artifact of collinearity with the democracy variable. Dropping the latter leads the variable u.s. aid per capita to be positively and significantly correlated with the dependent variable (model 4). A possible reason for this correlation is the greater likelihood for U.S. aid to be distributed to democratic than authoritarian regimes.Footnote ⁴²

Models 2 to 4 underscore the importance of two sets of variables: the raw security risk, whether measured by hostility or enduring rivalry, and the security guarantees with the exception of the Rio Pact. I have no ready-made explanation for the Latin American exception, other than referring to the love-hate relation that exists between the United States and its traditional zone of influence. The coefficients on the security and guarantee variables are significantly different from zero. Their estimated impact on the dependent variable is also substantial. The entries of Table 2 represent the percentage change in the baseline hazard rate for a given change in each explanatory variable of model 4. For example, a country involved in an enduring rivalry with a neighbor has a hazard rate for signing the NPT that is 41 percent lower than a similar country involved in no enduring rivalry. In contrast, a formal security guarantee from a superpower other than through the Rio Pact increases the hazard rate by 71 percent. U.S. financial aid also plays a role, though a more limited one: a one-standard deviation increase from the mean yields a puny 4 percent increase in the chance of ratifying the treaty. These results make it clear that exclusion is a function of rivalry between neighboring states and thus of compliance costs with the principal's goal of nonproliferation. Koremenos, Lipson, and Snidal'sFootnote ⁴³ idea that distributive problems at large can be solved by increasing membership is not observable in the nuclear proliferation regime.

TABLE 2.

Percentage change in hazards for statistically significant variables (Model 4)

Notes:

The change is calculated according to the formula: [(exp(beta*X₂) − exp(beta*X₁))/exp(beta*X₁)] * 100, with beta the estimated coefficient, X₁ and X₂ respectively the mean and the mean augmented by a standard deviation for continuous variables, and 0 and 1 for dummy variables. SD = standard deviation.

In accordance with predictions, the economic variables have a meaningful negative impact on the odds of ratifying the NPT, confirming the affordability hypothesis.

Among the control variables, the cumulative ratification index has no noticeable effect on the rate of ratification in model 4 and is wrongly signed in models 1 to 3, and thus does not support the view that states wish to conform. Only the end of the Cold War is significantly and substantively correlated with ratification, though the sign belies gloomy neorealist predictions—ratification received a boost after 1990. Rather than sapping the basis for the nonproliferation regime, the end of the Cold War led to a revival of the NPT. I further investigate the reasons for this revival in the next section.

Sanctioning Nonparticipants and Monitoring Participants

I now present anecdotal and systematic evidence for conjectures 3 and 4 related to the principal's ability to sanction (ρ) and monitor (1 − q). During the period 1977–91, the founders lost their capacity to sanction nonparticipants and monitor cheating. They did not offset the deficiency in this incentive by making the other incentives more powerful. As a result, the nonproliferation regime exhibited a loss in efficiency; it stopped attracting participants. In 1991, in contrast, the founders rebuilt this capacity; they also strengthened the IAEA safeguards and verification regime, resulting in greater participation.

The surprise explosion of an Indian device in 1974 led the founders to open their initial export cartel to other suppliers of nuclear fuel and technology. They founded the Nuclear Suppliers Group (NSG) and established the Trigger List, a list of material and equipment, the export of which they would regulate. From then on, however, the NSG fell into a state of, in one of his past chairman's words, “relative inactivity.”Footnote ⁴⁴ The supplier cartel broke up, divided between the three Anglo-Saxon countries (United States, Canada, and Australia), who held near-monopolist control on the supply of uranium, and France, Germany, Switzerland, and Belgium, who were willing to fill the demand for the construction of fuel facilities—uranium enrichment and plutonium reprocessing plants.Footnote ⁴⁵ Cooperation within the cartel came to an abrupt halt. The group did not meet for thirteen years. During that period, no change was made to the Trigger List, despite a pressing need for regular updating and extension to keep up with new technologies.

Compounding the erosion of the export controls regime was the ongoing weakness of the IAEA verification regime. The regime was admittedly weak from the start: time, frequency, and scope of inspections had to be prearranged with each government. Still, it was expected that the discovery of cases of noncompliance would call for and result in step-by-step strengthening. The thirteen-year lack of coordination among supplier states prevented this from happening, giving a headstart to would-be rogues. Iraq's first-attempt at getting the bomb—centered around the Osirak reactor and an Italian hot cell to separate plutonium—was to have been an NPT-safeguarded and regularly IAEA-inspected facility. After Israel bombed Iraq's reactor in 1981, Iraqi leader Saddam Hussein created a clandestine weapons program, which, despite employing seven thousand people, remained hidden from Western inspectors for nearly a decade.Footnote ⁴⁶

From a contractual perspective, the breakup of the cartel of suppliers modified the terms of the generic contract in favor of non-nuclear weapon states. Furthermore, the superpowers were not willing to make up for the weakening of the multilateral instrument by means of an active bilateral approach. The fall of the pro-American Shah in Iran and the Soviet invasion of Afghanistan in 1979 led the United States to take a more favorable attitude toward exports of fuel to India and Pakistan.Footnote ⁴⁷ The administration of President Jimmy Carter exempted India from sanctions, while the Reagan administration maintained full military aid to Pakistan until 1990.Footnote ⁴⁸

The 1977–91 years were bleak for nuclear nonproliferation. On average, fewer countries adhered to the treaty in that period. During this time, Brazil and Argentina, two nonsignatories, began their nuclear weapon programs, and South Africa, a nonsignatory, succeeded in building a nuclear device, while Libya, Iran, Iraq, and North Korea, four signatories, began cheating with their obligations under the treaty.

This dismal period came to an end in 1992, when the conjunction of long-trend effects (abundance of uranium, drying out of the market for nuclear power) and short-term emergencies (the Persian Gulf War and the subsequent discovery of unsuspected amounts of sensitive materials, equipment, and technology in Iraq) led France and Germany to rejoin the cartel and side with the U.S. desire to tighten up the regime. The list of sensitive items was expanded and export restrictions agreed upon thousands of items. The safeguards were tightened and the verification regime was strengthened through the 1997 Model Additional Protocols.Footnote ⁴⁹ The 1990s saw a readjustment of the terms of the regime in favor of the nuclear cartel.

As a result, more states either signed and ratified or complied. Indeed, the list of states that acceded as non-nuclear-weapon states included Argentina, Chile, and Brazil in Latin America; South Africa, Angola, Namibia, Zambia, and Zimbabwe in the southern tip of Africa; Tanzania and Algeria in the rest of Africa; and all the ex-Soviet Republics in Asia. With the possible exception of some ex-Soviet Republics, none of these countries received positive or negative incentives other than those included in, or implied by, the NPT.Footnote ⁵⁰

The hypothesis that the breakdown of the cartel led to a slack in joining rates is easily tested on the ratification dataset. To this end, I create the dichotomous variable 1977–91, coded “1” during the corresponding years and “0” otherwise. I merely introduce this variable in the prior data analysis, from which I remove the end of the Cold War variable 1991–2002 on the grounds that it corresponds, both statistically and substantively, with the rebirth of the cartel. Percentage changes in hazard rates for a given change in each statistically significant explanatory variable are reported in Table 3. The 1977–91 period exhibits a strong negative impact on ratification, with a level of ratification half of what it was in the prior and posterior periods. All prior results hold.

TABLE 3.

Percentage change in hazards for statistically significant variables (Model 4 modified)

Notes:

The change is calculated according to the formula: [(exp(beta*X₂) − exp(beta*X₁))/exp(beta*X₁)] * 100, with beta the estimated coefficient, X₁ and X₂ respectively the mean and the mean augmented by a standard deviation for continuous variables, while 0 and 1 for dummy variables. SD = standard deviation.

In sum, four of the comparative statics that were drawn from the model find some form of historical validation: the risk of exclusion increases with (1) high compliance costs, (2) high opportunity costs, (3) poor sanctioning of nonparticipation, and (4) poor monitoring of compliance. These predictions are fairly intuitive, but given that they were all drawn from the theory, their empirical validation strengthen our confidence in the ability of the theory to explain the three-tiered structure of the nuclear proliferation regime.

Currency

The role of transaction costs in regulating the relative importance of multilateral and bilateral instruments is visible in currency regimes. Bretton Woods consisted of a multilateral agreement signed in 1944, featuring a common positive incentive—the possibility to draw resources from the International Monetary Fund (IMF)–and various bilateral arrangements between national treasuries.Footnote ⁵¹ In contrast, the gold standard in its heyday featured no multilateral instrument proper but consisted mainly of various informal arrangements between central banks. It is only after World War I that the regime became a matter for negotiations at international conferences.Footnote ⁵²

The ratio between multilateral and bilateral components thus differed markedly between the two regimes: whereas Bretton Woods was run through the IMF according to rules consigned in the agreement, the gold standard essentially was run by central bank governors meeting one another on an ad hoc basis whenever they felt the need to. The principle of gold convertibility was commonly shared without having ever been sanctioned by an international conference because relations between governments were delegated to and mediated by financial markets, a mechanism apt to minimize transaction costs.

Today's international currency regime resembles the gold standard. There is no institutionalized multilateral regime beyond the occasional Group of 8 (G8) meetings among the major currency countries, while the IMF's role is limited to helping peripheral countries. Most of the bidding is made in global capital markets.

An effect of market mediation was, and is, to minimize the agent surplus that characterized Bretton Woods. Countries that were capable of monetary discipline still preferred to pursue liberal growth policies on the grounds that in case of emergency they could always avail themselves of the resources that were initially put in place for countries with less flexible domestic constituencies—a choice that eventually fueled worldwide inflation. Under market mediation, national treasuries pay interest rate premiums that closely reflect their monetary policies. Although more efficient, market mediation was not available in the postwar era because banks and securities markets were strictly regulated.Footnote ⁵³ The multilateral agreement helped overcome problems of coordination among treasuries, which were held responsible for the collapse of the gold standard in the interwar period.

Trade

The notion of transaction costs that I have used so far is restricted to the contractual costs of bargaining usually expended in time, transport, hotel, and legal assistance, which can be substantial given the multiple rounds it often takes for each side to figure out their respective reservation value. Although present in trade negotiations too, these costs take second place to another kind of transaction costs known as externalities. Under the modern trade regime, any bilaterally-negotiated tariff reduction is extended to all other parties on the basis of most-favored-nation (MFN) treatment, potentially lessening the benefit that any country may expect from entering into a bilateral negotiation in the first place. As a result, negotiators have an interest in free riding on one another and few deals get made. The solution to externalities of such kind is a multilateral negotiation in which trade partners follow an inflexible bargaining rule such as a 10 percent cut across the board, cuts proportional to current level of protection, or what not.Footnote ⁵⁴

While the inflexible rule approach addresses the externality problem (in a way that parallels how multilateral bargaining addresses the transaction cost problem), at the same time it presents the drawback of forcing the negotiations into a suboptimal outcome, since cuts no longer reflect each economy's relative comparative advantages and marginal costs, but are homogeneous across trade partners, causing an agent surplus cashed in by those who would have made the same cuts for less in return. This is the reason why, whenever externalities were tolerable, negotiations within the General Agreement on Tariffs and Trade (GATT)—and a fortiori outside the GATT in the form of voluntary export restraints (VERs)—were conducted on a “principal supplier” basis, whereby “a country could be requested to make a concession on a product only by the partner which provided the largest share of its imports.”Footnote ⁵⁵

The trade-off between externality and agent surplus gives one a sense of the relative role of multilateral and bilateral negotiations within the GATT. Consider a country like the United States, a group of trade partners, and a given basket of products. The United States would want to engage in an inflexible multilateral round of negotiations with suppliers of products for which it does not have a principal supplier, thereby limiting externalities, while it would want to have bilateral talks with suppliers of products for which it does, thereby limiting the agent surplus. Of course, the fact that the United States is also a supplier and that all countries are in this dual position may complicate the calculations, but it does not change the comparative statics of the institutional equilibrium, making room for bilateral negotiations when externalities, that is, transaction costs, are low in order to minimize the agent surplus.

It is interesting to note that within the GATT/WTO, all enforcement, whether it is mandated by panel rulings or pursued outside of the legal framework (for instance, through “Section 301”), is done bilaterally. There is no multilateral sanctioning mechanism within the trading regime.Footnote ⁵⁶ While some have been eager to see something in enforcement that would make it bilateral rather than multilateral, note that one-on-one retaliation does not work in matters of proliferation, which calls instead for export control groups—the NSG in the nuclear regime, the Australia Group in the chemical and biological regimes, the equivalent body in the Missile Technology Control Regime, and the granddaddy of all, the Coordinating Committee on Multilateral Export Controls (COCOM).Footnote ⁵⁷

Aid

A key assumption of the model is the market analogy: the multilateral instrument treats all members in the same way, while the bilateral instruments, in contrast, allow for market fragmentation. This assumption is useful in regimes such as nuclear proliferation, currency, trade with MFN treatment, and probably many other regimes, but not in the aid regime. Aid, whether multilateral or bilateral, can be made to reflect the recipient's needs. As a result, the present model, applied as is, would predict that all aid should be multilateral because it has the advantage of minimizing transaction costs without the drawback of generating an agent surplus, since each recipient is (or could be) given to according to needs. Of course, this is not the case: no more than a third of all aid is estimated to be multilateral.Footnote ⁵⁸ The mechanism responsible for the multilateral-bilateral structure in the aid regime calls for further analysis.

Recipient's need is the wrong dimension on which to classify countries. Recent studiesFootnote ⁵⁹ have made patent what one always suspected: the need for aid plays second fiddle to the recipient's strategic, political, or trading usefulness to the donor, with the result that bilateral aid, unlike multilateral aid, is almost always politicized. Moreover, the two dimensions of need and usefulness are negatively correlated, and this for two reasons: first, the poorest countries are also those that are the least likely to be useful to rich donors; second, the poorest countries offer a greater developmental bang for the buck—morally, if not economically—than wealthier ones. As a result, Milner notes, “multilateral aid tends to be given to poorer countries on average than does bilateral aid.”Footnote ⁶⁰

Analytically, the marginal gain of aid to the donor is one of two marginals. It is either the marginal developmental gain, which is obtained through multilateral aid and decreases with the recipient's wealth, or the marginal political gain, which is obtained through bilateral aid and increases with the recipient's wealth. The level of recipient's wealth at which these two marginals are equal defines a cutpoint below which the donor prefers multilateral aid to bilateral aid and beyond which the donor's preference switches to bilateral aid.

For a visual representation of this cutpoint, consider Figure 5, mapping the recipient's wealth on the horizontal axis and the donor's various marginal gains on the vertical axis. The descending curve maps the donor's marginal developmental gain of one dollar of aid as a function of the recipient's wealth, while the ascending curve maps the marginal political gain. The donor's marginal gain is maximized with multilateral aid up to the intersection point and with the addition of bilateral aid thereon. This intersection point corresponds to the x of the proliferation regime model, while the y falls to the right of x at a level of wealth past which it no longer is considered reasonable to ask for, or hand out, aid.

FIGURE 5.

Structure of the aid regime

Therefore, only bilateral aid can be customized to the donor's political goals. The attribution of multilateral aid, in contrast, obeys fixed, impersonal criteria, over which individual governments have limited or no control. It is this second-order rigidity—the fact that all recipients have to be treated according to the same rules—that makes the member-surplus problem applicable to multilateral aid. Efficient for the most underdeveloped recipients, from which hardly any favor can be had, the multilateral mode of allocation becomes inefficient with countries that present donors with greater strategic or diplomatic opportunities. Rather than raising incentives for all recipients, donors prefer to customize incentives to targets of special interest to them. For instance, although both the United States and Europe value the protection of human rights and use aid to promote it, they have different geographic priorities, reflecting different colonial histories, inherited contacts, physical proximity, unresolved differences, and bargaining leverage. They use bilateral aid to foster human rights in their respective areas of influence.

In sum, the aid regime presents the same three-tiered structure as the nuclear proliferation regime. It can be modeled as a principal-agent contract and the logic for the cutpoint between multilateral and bilateral aid indirectly reflects the same member-surplus rationale, which I found to be at work in the NPT, currency, and trade regimes. Generally, to the extent that any multilateral regime treats members according to a set of fixed, impersonal criteria, it creates an inefficiency in the form of an agent surplus—a surplus distributed to members with compliance costs well below incentive levels set by impersonal rules.

Other Approaches to the Nuclear Proliferation Regime

Existing studies do not seek to explain membership in the NPT regime but focus instead on the decision to pursue nuclear weapons programs or acquire nuclear weapons.Footnote ⁶¹ While nuclear proliferation has been given a good deal of scrutiny in the literature, I wish to restrict this survey to two approaches—quantitative and interpretive—that have recently received attention.

On the quantitative side, three studiesFootnote ⁶² agree on the importance of technological determinants, economic capacity, and the existence of a security guarantee in the decisions to launch a nuclear research program and acquire and deploy nuclear arms. Of the three, the two more recent studies assess the relevance of NPT membership to proliferation: while they both find a statistically significant negative relation between accession to the treaty and developing nuclear weapons, Jo and Gartzke also test for what they call the “systemic effect” of the regime, proxied by the number of total ratifications, and find no relation. They conclude that “these results cast doubt on the validity of constructivist arguments about the transformative effect of international agreements at the system level… .”Footnote ⁶³

The present analysis replicates most of these econometric results while using accession as a dependent variable, suggesting that the decisions to proliferate and join the NPT can be viewed as one and the same. The present study, however, cautions against Jo and Gartzke's conclusion that the regime is irrelevant. Their non-finding only applies to the multilateral component of the NPT regime, which they test against the bilateral component (the existence of nuclear guarantees). Not surprisingly, they find the latter to be both significant and important in predicting the launching of a nuclear program, but too hastily credit the finding to realpolitik in contradistinction with the regime, overlooking the fact that nuclear guarantees are a key component of the regime as a whole.

On the interpretive side, a new set of studies have portrayed nuclear proliferation as the new threat that has come to dominate the security discourse in the wake of the disappearance of the Soviet threat.Footnote ⁶⁴ The “securitization” of proliferation and the demonization of proliferators as “rogue states,” these authors argue, further distanced the NPT regime from disarmament, which, along with nonproliferation, was among its initial goals. This trend has fueled the antagonism of developing countries led by India, who denounce the discrimination between the nuclear haves and the nuclear have-nots. According to Mutimer,Footnote ⁶⁵ the current framing of proliferation as the main threat to world stability constitutes the main reason for India's consistent refusal to sign the NPT and its more recent refusal of signing the Comprehensive Test Ban Treaty.

This line of argument in many ways dovetails with the present analysis, which, more than any other, demonstrates the importance of bilateral security guarantees to the working of the regime. Security guarantees would not be credible if the guarantors were considering serious disarming. The drop in the credibility of Soviet security assurances in the late 1980s and their official withdrawal in 1991, for instance, had negative consequences for the NPT regime, prompting the acceleration of nuclear programs in North Korea, Iraq, and Iran.Footnote ⁶⁶ Given the negative effects that disarming would have on guarantees, the price that India asked in order for its government to sign the NPT—disarmament—exceeds what the superpowers are willing to pay.

The difference, if any, between the interpretive argument and the present analysis resides in the future consequences of the Indian exclusion. Interpretivists may see it as the discursive basis for the mobilizing of widespread opposition among developing countries. I see it as an uncharacteristically high cost of compliance, affecting only India and a handful of countries finding themselves in a situation similar to that of India.

Proposition (1)

The principal's problem is to solve program P ¹ as specified in the text. Assume that λ,θ,γ,ψ,π ≥ 0 are the Lagrangian parameters for each constraint in the order they are listed in P ¹. The Kuhn-Tucker conditions are twofold: (1) a nonbinding constraint implies that its corresponding parameter is zero—call it KT1; (2) a positive parameter implies that the constraint is binding—call it KT2. Forming the Lagrangian and deriving the first-order conditions with respect to a,d, and s yield

(FOC^a)

(FOC^d)

(FOC^s)

I do not solve the problem for all possible equilibria, but for one only, the mixed-incentive equilibrium.Footnote ⁶⁹ A mixed-incentive equilibrium by definition is of the form a,d,s > 0, implying by KT1 that γ,ψ,π = 0. These zero values along with FOC_d and FOC_s imply that λ,θ > 0, in turn yielding by KT2 the following system of three variables and two equations:

Two variables are endogenously determined as a function of a given third. I choose to express both a and s as a function of a given value of d yielding the results listed in proposition (1).

To establish the parametric conditions under which the mixed-incentive equilibrium obtains, subtract FOC_d and FOC_s and then the result from FOC_a. Recalling that γ,ψ,π = 0, the calculation yields the unique circumstances of the mixed incentive equilibrium, 1 = δ + σ; the marginal cost of the positive incentive is equal to the sum of the marginal costs of the negative incentives.

Proposition (2)

The principal now faces N dyads numbered according to the rivalry index z _i from 1 to N, such that z ₁ = 1, z ₂ = 2,…, z _N = N. z is distributed over the set (1,N] with , the set of positive integers.

Following lemma 1, assume that x and y partition the z segment into three sets, multilateral from 1 to x, multi-bilateral from x + 1 to y, and exclusion from y + 1 to N. A mixed instrument regime in equilibrium must satisfy the following set of inequalities: 1 < x* < y* < N. This requires that x* and y* be internal maxima. Were the principal's objective function continuous, identifying such maxima would directly follow from showing concavity. Since the function is not continuous, additional cases must be considered.

First, I calculate U _P in program P ^N as specified in the text. The summation term is equal to . Substituting this expression into U _P along with the value for g(x) and rearranging yields

One can now prove proposition (2).

Similar reasoning for y*|x yields , , and four different cases.

Furthermore, assuming the particular case in which and , equilibrium values x* and y* must satisfy 3 constraints:

Comparative Statics

Despite discontinuity, comparative statics is possible on U _P because it is monotonic in all its parameters. ; . ; . ; . ; if the sum of the marginals on the delivered incentives is greater than the sum of the marginals on the threats (1 + ρ ≥ δ + σ). ; , with if and otherwise. ; . ; , with . ; .

TABLE A1.

List of variables