CIAO DATE: 6/00

Nuclear Arsenal Games: Size Does Make a Difference

Carolyn C. James

International Studies Association
41st Annual Convention
Los Angeles, CA
March 14-18, 2000

 

I. Introduction

The purpose of this article is to present and establish the significance of the Nuclear Arsenal Game (NAG). The NAG investigates behavior within dyads experiencing a crisis. It assumes that nuclear and quasi-nuclear states act according to the size and potential of their own nuclear force structure and that of their opponent. This paper will argue that the size and potential damage an arsenal poses, set in relation to an enemy state's second strike capability, determines actor preferences within a crisis situation. These preferences include the option of launching a first strike and risking retaliation in kind. The specific objective of this study is to propose a nuclear index for use in empirical studies and offer a game-theoretic model of crisis interaction based on the Theory of Moves (TOM) that (a) encompasses these respective types of nuclear states; and (b) indicates whether preferences and predicted behavior adhere to the assumptions of Classical (or Rational) Deterrence Theory.

The definition of an international crisis used in this study is taken from Brecher and Wilkenfeld's well-established International Crisis Behavior (ICB) Project: "(1) a change in the type and/or increase in the intensity of disruptive, that is, hostile verbal or physical, interactions between two or more states, with a heightened probability of military hostilities, that, in turn, (2) destabilizes their relationship and challenges the structure of an international system — global, dominant or subsystem". ₁ Conflict can be either "verbal or physical". The crisis can be prior to use of force or intra-war in nature. Therefore, it is important to recognize that mutual cooperation is defined as the absence of nuclear use rather the absence of conflict itself. Crises in which the decision to escalate a conflict from conventional levels to nuclear are included alongside crises in which states have not yet resorted to arms.

It is necessary to begin by asking, among states that have chosen to proliferate, what is their nuclear weapons capability? Four levels of nuclear capability are defined alongside three sets of crisis preferences to serve as a starting point. It is predicted that nuclear capability has a direct connection to crisis preferences and crisis stability.

The four types of nuclear and quasi-nuclear arsenal states are as follows (see Table 1): mini-arsenal, third-, second- and first-level capability. ₂ The first level also is known as a "super-arsenal". Super-arsenal states are typified by the extreme redundancy within the nuclear force structures possessed by the United States and the Soviet Union/Russia. These arsenals are the basis for crisis behavior preferences that exemplify mutually assured destruction, or 'MAD'. A condition of MAD has been depicted as a stable relationship based upon a 'balance of terror'. ₃ Neither state would escalate a crisis to nuclear levels for fear of second-strike annihilation to both the state and society. Super-arsenals, possessing thousands of weapons ₄ , are capable of exacting second-strike assured destruction at a global level.

The second-level capable state possesses hundreds, not thousands of weapons. These states can threaten second-strike assured destruction of the state, and perhaps the society, of a rival within a single dyad. France, Great Britain, and China are second-level capable states. Their destructive capacity is enormous, but does not reach the level of, for example, the global nuclear winter expected to occur following an all-out super-arsenal attack.

India, Israel and Pakistan are examples of third-level arsenal states. They possess dozens of weapons. India and Israel, in fact, may be closer to a second-level capability as their arsenals may have exceeded 100 or more at one time or another. These arsenals, in a second-strike scenario, can defeat an enemy state within a single dyad, but may not reach the level of devastation that would destroy its opponent's very society.

'Mini-arsenal' is a concept developed to present more specifically a minimal nuclear capability and its relation to crisis behavior. ₅ This is perhaps the most complex, and therefore difficult, level to describe. First, a mini-arsenal state is capable of acquiring at best, two or three, crude Hiroshima or Nagasaki-style warheads. Fat Man, the bomb dropped on the city of Nagasaki, was the more powerful of the two at about 20 kilotons. This pales in comparison to thermonuclear weapons, that are measured in megatons. India, Israel and Pakistan, which can project significant nuclear threats, are beyond this category since the arsenals they are believed to possess contain qualitatively and quantitatively much more destructive power. Second, the most critical distinction of the mini-arsenal is that while potential damage may be extreme, destruction of state or society is not assured. A strike from a mini-arsenal state may be survivable — militarily, politically and socially. This perception, which may be held both by the mini-arsenal state leadership and its potential enemies, is expected to result in preferences and behavior that do not match actions of states with more deadly arsenals. Leadership that is more willing to risk domestic populations may consciously choose to escalate to nuclear levels if the state and its government may survive. ₆ Of the four levels of nuclear capability, mini-arsenal dyads promise to be the most unstable during crises as the deadliest of cost-benefit analyses is expected to take place.

The NAG assumes that capability is related to, yet distinct, from choice. Canada and Sweden, for instance, have the capability to proliferate with relatively few physical impediments. Resources, in particular human talent and fissile material, are either available or can be procured. These states are not included in the subsequent analysis since they currently do not have a policy of proliferation. At present, they have chosen not to exercise their nuclear capabilities towards weaponization. Iran and Iraq, as will be seen below, have decided to pursue proliferation. They are restricted, however, by limited resources, meaning that they have a limited capability. The desire exists to move to higher levels of nuclear ability, but this desire is inhibited.

One final point needs to be made. A state's capability, in particular a mini-arsenal capability, is not assumed to be static. States have exhibited a nuclear 'learning curve' and increased capacity to, for example, produce fissile material domestically as these industries grow and mature. At this turn of the century, the reality of proliferating states, which are often poor and underdeveloped, is that desire and capability are ill-matched. Their condition of mini-arsenal capability has been extended, in part, by restrictions that prohibit more rapid proliferation. In addition, policies from external actors have failed to provide a substitute for the internal motivations to acquire nuclear force structures.

Hence, the study includes but differentiates between states that are entrenched in a mini-arsenal capability and those that temporarily are passing through a period of initial weaponization and can expect to reach higher levels within a relatively short span of time. Consider, for example, the United States between 1945 and 1949. By the end of 1945, the United States had six warheads and fifteen bombers able to deliver them. In 1946 the number increased to eleven and 125, respectively. By 1949, the year in which the Soviet had its first and, at that time, only deliverable warhead, the United States had an arsenal of over 200 warheads and over 400 bombers. The Soviet would catch up quickly, breaching the 200-warhead mark in stockpiled warheads in 1955. However, it was not until 1956 that they had a strategic force loading capability, defined as independently targetable warheads associated with total operational ICBMs, SLBMs or long-range bombers. ₇

Since 1945, when the first and only nuclear attacks occurred, serious contemplation of engaging in a nuclear exchange has seemed implausible to most observers inside and out of the military, the policymaking community and academic circles. It potential costs are so high, that any 'rational' actor would be deterred. In fact, the absence of a nuclear war, or a global conflict of any kind, apparently lends credence to theories of robust nuclear deterrence and peaceful democracies. Absence of a phenomenon, however compelling, cannot prove that a correlation exists, determine its causal directions with true certainty or negate the effects of other variables. The simple truth is that the nuclear genie is out, and the potential for a nuclear exchange exists as long as the weapons can be deployed. Whenever this scenario exists, or even remains possible, it is critical to explore under what dynamics potential use can become a reality. Only then can the goal of preventing a nuclear exchange be approached with confidence.

Studies to date usually have manifested, whether consciously or not, an assumption of super-arsenal dynamics for both parties to a dyad. The Cold War has left an enormous legacy of literature that focuses on the United States, the Soviet Union, and their respective nuclear force structures. In large part, nuclear strategy and doctrine have been observed and analyzed according to super-arsenal realities. ₈ Not all states, however, can be classified as super-arsenals. Crises such as the 1962 Soviet deployment of nuclear-tipped missiles in Cuba may or may not have the same non-nuclear results. ₉ It is inappropriate, even dangerous, to assume that all states in crises will react in the same manner with the same non-nuclear results. 'Rational' determinations of cost and benefit may not match those made under super-arsenal threats. The necessary foundations of stable deterrence may exist, but fall short of sufficiency. ₁₀ The 'MAD' game of 'Chicken', often depicted as an appropriate metaphor for the Cold War relations between the two superpowers, ₁₁ may not be played within other crisis dyads. In particular, mini-arsenal dyads that do not promise assured destruction of state or society, may be prone to risking the collision that the United States and Soviet Union avoided.

Rational Deterrence Theory, one of the by-products of Cold War strategic thought, often carries super-arsenal assumptions of assured destruction. ₁₂ Rational decision-making under the veil of nuclear threat may not always exhibit super-arsenal logic. ₁₃ In other words, it is not sufficient to assume that states within nuclear crisis dyads, regardless of level, will play the 'rules' of Chicken and MAD. More importantly, this paper rests on the tenet states considering nuclear use, within dyads that fall short of assured destruction, should not be classified as irrational. Nuclear Arsenal Games, a game-theoretic model, allows a variety of alternate preference orderings and a testing program that includes rivalries beyond the US and USSR. ₁₄

This initial exercise in NAG begins with the opposite end of the spectrum from super-arsenals by examining a mini-arsenal dyad within the Northern Tier. Both Iran and Iraq meet the criteria of mini-arsenal capable states, in this instance still believed to have quasi-nuclear status. Both could be successful proliferators in a quite short period of time if certain critical conditions change even slightly. ₁₅ Iran and Iraq are particularly suited for this inquiry since their history provides multiple cases for crisis interaction and behavior observance. ₁₆

The paper proceeds with an overview of Classical Deterrence Theory, the dominant nuclear use theory during the Cold War. Section III offers a brief review of the United States' policies against nuclear proliferation in Iran and Iraq since the collapse of the Soviet Union. US policy is chosen since it often has led nonproliferation efforts and has a history of active involvement in the Northern Tier. The key role of exogenous policy in creating or avoiding crisis instability will be emphasized. The paper will argue that US policy inappropriately continues to extend super-arsenal assumptions, and therefore logic, indiscriminately toward all states. The US insistence on depicting actors who consider nuclear use as necessarily 'irrational' is criticized. On the other hand, it will be argued that the assumptions of Classical Deterrence Theory, in particular rational decision-making, hold and provide useful insights when crisis actors and their preferences, regardless of nuclear capability, are properly assessed. The level of perceived threat that exists when destruction is not assured can appear acceptable, even prudent, during a crisis in relation to other alternatives.

It outside the purpose of this paper to determine exact levels of acceptable costs for a given actor. The purpose for applied research on NAG is not to set these levels; rather it is to allow testing of a variety of views in order to determine preferences that are most conducive to crisis stability, measured as non-nuclear use. Levels of nuclear capability, reflected in rational cost-benefit analyses and the preferences they produce, are incorporated in the NAG model presented in Section IV. The TOM is used as an example of one game-theoretic approach that can trace potential behavior for states in the game who base decisions on alternative preference orderings. One set of potential preferences are presented for Iran and Iraq and used to illustrate the NAG's heuristic potential in understanding crisis behavior and tailoring policies toward stability. Various policy alternatives will be offered in the concluding section, along with summary remarks about the NAG.

 

II. Classical Deterrence Theory ₁₇

Jervis describes deterrence theory as the "most influential school of thought in the American study of international relations". ₁₈ It is not surprising, nor is it a novel idea, that the development of the theory typified a bipolar, Cold War world with the United States as one center of power. The premise of deterrence theory is simple. One state acquires sufficient power, and exhibits the necessary resolve to use that power, in order to influence a potential adversary against an aggressive act. Classical Deterrence Theory often is used to try to determine how best to establish an effective deterrent situation. It can be equally valuable by showing where deterrence does not work. Rational deterrence theory, properly applied, can indicate cases in which potential nuclear use might pass outside "the threat that leaves something to chance". ₁₉ Once identified, and dealt with as a result of a rational decision-making process, policy can be tailored in the effort to prevent nuclear use of force.

A nuclear force structure may be viewed as a desirable possession when deterrence becomes a state's policy, since military power can be increased exponentially over conventional forces. ₂₀ Calculated in terms of TNT, the destruction at Hiroshima and Nagasaki could be compared to the fire bombings of Dresden and Tokyo. "'Nuclear' is not synonymous with 'unlimited', nor 'conventional' with 'limited'". ₂₁ There are differences, however, which place nuclear weapons in a separate class, even from some biological and chemical 'weapons of mass destruction'. Rhodes offers five effects that increase the 'ease of inflicting pain' over unlimited conventional warfare: lower economic and social costs, no direct correlation with traditional military victory, speed, physical concentration of power and negative effects on decision-making processes. ₂₂ This appears to match super-arsenals quite well, but can this also be said for lesser levels of nuclear capability? How exactly does the theory relate to the weapon? It is not a perfect fit.

One of the keys to Classical Deterrence Theory is the concept of 'rationality'. When the possibility of nuclear use has been a factor, rationality has been one of the most debated components of deterrence. The arguments manifest various forms. First, there is the question of whether or not rationality properly belongs in deterrence theory at all when nuclear weapons are part of the scenario. Morgan and Zagare, in spite of their contrasting methodologies, both consider rationality contrary to deterrence. ₂₃ Taken in its purest form of threat, how could any rational decision-maker risk total annihilation to both state and society? Yet, nuclear deterrence of the Cold War, East-West variety depicts just such a scenario. If the United States attacked the Soviet Union, the Soviets' secure second-strike force would retaliate, and vice versa. Morgan, therefore, points out the contradiction between a state's effort to establish controlled and deliberate decision-making versus the necessity of projecting the seemingly irrational capability of launching, and subsequently suffering, a nuclear attack. Couched in the language of game theory, Zagare has made the argument that 'Prisoner's Dilemma' and 'Called Bluff' more accurately describe superpower deterrence behavior than a zero-sum version of 'Chicken', the game most often used to depict the dynamics nuclear deterrence. ₂₄ He argues that Prisoner's Dilemma reflects MAD, since no state would choose non-cooperation in Chicken's worst-case scenario of (1,1) — or mutual annihilation. However, mutual non-cooperation in Prisoner's Dilemma is (2,2), the second worst outcome, and therefore a credible deterrent strategy. In this case, being hit unilaterally is perceived as worse than an exchange. ₂₅

One way out of this intellectual dilemma has been proposed by Schelling, who suggests that it is rational to feign being irrational. ₂₆ Jervis asserts that there need only be a chance that a state would engage in nuclear war for the threat to become effective. ₂₇ The simple possibility is sufficient to deter. ₂₈ This idea is the foundation to concepts such as 'existential deterrence', which theoretically functions when there is any possibility of escalation to nuclear levels. ₂₉ Here again there is a dichotomy of opinion among deterrence scholars. Nuclear 'optimists' believe the potential destruction resulting from a nuclear attack will prevent such an occurrence, even accidentally. ₃₀ 'Pessimists' warn, however, that nuclear use is quite possible, stemming from weaknesses in individual decision-making to organizational proclivities. ₃₁

Some scholars couch the question of nuclear use in terms of escalation and limited war. Smoke defined escalation as "the process by which the previous limits of a war are crossed and new one established" and "limits of a war are the barriers or thresholds or stages of the escalation process". ₃₂ Applied here, therefore, the 'limited' nature of war is hoped to remain conventional only, with escalation 'crossing' into nuclear realms. ₃₃ Kahn used the metaphor of an 'escalation ladder'. ₃₄ Meant as a methodological tool rather than a comprehensive theory of all crises, the ladder has a total of 44 rungs states that can move from "subcrisis maneuvering" to "spasm or insensate war". Kahn places the 'threshold' for nuclear use at the 21st rung, an "exemplary" local nuclear war in the category of "bizarre crises". ₃₅ However, at the previous 15th rung, "barely nuclear war", "one or more nuclear weapons may be used unintentionally (accidentally or unauthorized). Or one of the antagonists may make military or political use of a nuclear weapon but try to give the impression that the use was unintentional". ₃₆ Fully intentional use at rung 21, however, would clearly break the 'nuclear taboo'. ₃₇ Kahn's ladder of escalation, taken to the top, typifies the capability of a super-arsenal. Most states could not progress that far, due to a more limited nuclear capability. Mini-arsenals, for example, could expend their entire nuclear force in one or two strikes. Using the ladder metaphor, if a function of nuclear escalation is to probe the possibility of keeping a war limited while maintaining the threat of a general nuclear war, then clearly some nuclear-capable states would be restricted to shorter ladders.

Freedman points out that Kahn's ladder provides a particularly significant prediction. Nuclear use is possible under controlled and rational decision-making. Even seemingly irrational acts are performed for rational purposes. "Asymmetry of capabilities" as a source of power is critical. The actor either more able, or more willing, to move up the ladder would have increased bargaining power. ₃₈

The related problem of unintentional escalation is highlighted in the Sagan-Waltz debate between nuclear 'optimists' and 'pessimists'. Waltz, an optimist, lists three requirements for successful deterrence by "small nuclear forces": (1) a secure second strike capability without (2) the necessity for early firing (in response to a false alarm) and (3) reliable command and control to avoid accidents or unauthorized launches. There still exists, however, the assumption (not stated by Waltz as a requirement) to inflict unacceptable damage. ₃₉ One or two fission weapons striking Moscow would have been enough to deter the Soviet Union. ₄₀ Again the analyst is faced with the decision to describe any nuclear use as unacceptable, or to consider 'rational' nuclear use corresponding to multiple capabilities among actors. Current studies rarely make this distinction, and therefore do not offer evidence to support Waltz's argument.

Sagan, using organization theory, argues that weaknesses exist that may result in unreliable command and control. ₄₁ For example, when one state has acquired a nuclear force structure and a potential enemy is approaching nuclear capability, military leaders probably would want to launch a preventive strike. Israel did just that in 1982 when they bombed Iraq's Osiraq reactor before it could produce weapons-grade fissile material in sufficient amounts to allow the Iraqis to proliferate. In 1954, a Joint Chiefs of Staff report to President Eisenhower advocated a preventive war against the USSR before they had achieved the ability to launch a massive strike against the US, ₄₂ a capability they reached in 1956. In other instances, leadership may not respond the way the American president did at that time.

Allison, Carnesale and Nye add a category to the nuclear pessimist/optimist dichotomy. ₄₃ They list three ways to avoid nuclear war according to their respective proponents: "hawks, doves and owls". Hawks resemble nuclear optimists. They believe a state should bargain from strength, showing a firm resolve to use a nuclear deterrent. Doves manifest some aspects of pessimists, in that they fear arms races may actually weaken deterrence and advocate a policy of accommodation. They differ from many pessimists in their assumption, shared with hawks, that there is a rational decision-making process. Owls represent the pessimist concern about the many factors that can impede rational decision-making, such as poor information, errors, stress and organizational biases. However, the discussion, published in 1984, relates to super-arsenal, Cold War states.

Nuclear use through rational decision-making can occur under other circumstances. A state may take nuclear chances by, in a sense, playing the odds. ₄₄ In fact, it would be rational to do so if leadership is convinced that, once threatened, the other side is highly likely to back down. This tactic obviously benefits a non-status quo state, since a state predicted to accept the current situation rather than suffer loss would be more likely to succumb to nuclear intimidation. This argument, however convincing, matches many others, in that a distinction among levels of nuclear capability is not made clear.

Deterrence theory, if it truly does function in the ways described above, possesses neorealist attributes of international relations. ₄₅ Deterrence theorists can be divided into two basic groups: Structural (or Neorealist) Deterrence Theorists and Decision-Theoretic Deterrence Theorists. ₄₆ The Neorealists identify the distribution of power as the best explanatory variable in the causal relationship between system structure and stability. ₄₇ Therefore, the destructive power of nuclear weapons, coupled with a bipolar systemic structure, would be the primary cause of Cold War stability. ₄₈ Given these assertions, it logically follows that between nuclear-capable adversaries, bipolarity is more stable than multipolarity with nuclear weapons offering a defensive advantage. ₄₉

Intriligator and Britos' formal model of a missile war exhibits the assumptions and implications of Structural Deterrence Theory (see Figure 1). ₅₀ The model posits that effective deterrence ultimately is determined by the level of costs. To determine costs, some kind of assessment needs to be made about an opponent's potential projection of power. This model suggests that 'bean counting' should become the hallmark of determining relative power, which logically includes knowledge of the kinds and amounts of weapons and delivery systems within a nuclear force structure. Assuming the neorealist world of unitary, self-interested, power-maximizing states, the option to use nuclear weapons will be deterred if the costs of a second strike retaliation exceeds potential benefits. In these situations, balance with high potential costs encourages stability, balance with low potential costs can be unstable, and imbalance alone is unstable, but particularly so when costs are low and preemption is attractive.

The model's Trajectory 1 (arrow 1) indicates low costs, but also may be interpreted as an area of possible conflict, or escalation to nuclear levels. As a state begins the initial move from (0,0), it enters a "region of initiation". If this were compared to nuclear proliferation, Trajectory 1 depicts the earliest stages of nuclear weapons possession as existing in the same "region of initiation". We find two kinds of states in this zone. The first are technologically advanced states that have chosen to proliferate. It is a temporary phenomenon; the only element placing the state in the region of initiation is time. In other words, they are just beginning to construct their nuclear force structure. It is assumed that the state can move quickly toward possessing more significant arsenals. The other kind of state is, again using the parameter of time, trapped in this zone. They can be relatively permanent mini-arsenal states, with permanence referring to a period of time that may extend for several years, or even decades.

In the vast majority of literature to date, however, nuclear forces are typically presented as either in existence or not in existence. This tendency is seen in the assumptions made in descriptive case studies as well as in the coding used in quantitative analyses. A widespread assumption has been that any nuclear strength automatically places potential costs above any potential benefits for a 'rational' decision-maker.

Many states are not nuclear-capable as a matter of choice, rather than a result of economic or technical poverty. A majority of these states claim to be inhibited by the international norm against nuclear proliferation established, in large part, by the components and efforts of the Nuclear Nonproliferation Regime. ₅₁ If, however, a state is willing to risk international censure and attempt to proliferate, it may be forced to remain at a mini-arsenal level, or Intriligator and Brito's dangerous zone of initiation. In this scenario, nuclear deterrence cannot be established in a manner that can guarantee nuclear-free crises.

It may be in recognition of this possibility that some scholars are intrigued by the "more is better" argument, a hallmark of Waltz. ₅₂ Again in accordance with Structural Deterrence Theory, the proposal to be tested is that safe and selective proliferation would actually enhance systemic stability in certain cases. ₅₃ Zagare points out that Structural Deterrence Theorists usually qualify this point by making an exception of "crazy states" and "irrational leaders". ₅₄ This is the juncture at which this paper departs from the bulk of deterrence literature. What if a state possesses, for example, a mini-arsenal, and therefore cannot ensure a level of destruction that sufficiently threatens an adversary? What if the ultimate cost to the opposing decision-maker is personal power rather than casualties? In a rational cost/benefit, self-maximizing calculation, risking nuclear retaliation may appear to be a valid option. In this case, the assumption that any level of nuclear attack is sufficient to deter, even of the kind Japan suffered in 1945, might be dangerously inaccurate.

The Decision-Theoretic Deterrence Theory cited above evolved from Structural Deterrence Theory. Decision-Theoretic Deterrence Theorists accept the conclusions drawn by Structural Deterrence and build on them to provide an analysis of decision behavior. In other words, they begin with the assumption that any nuclear war is too costly to be fought. Concepts derived from this school include "critical risk", or the maximum point of acceptable punishment before a decision-maker is deterred. ₅₅ In a crisis, the state with the lowest threshold for pain would 'blink', or swerve, first. Tactics based on this opinion can easily be translated into a state's functioning policy. These could include convincing your adversary that you are incapable of making concessions, ₅₆ feigning irrationality, ₅₇ or Kahn's dramatic metaphor of ripping the steering wheel from the car while engaged in a game of Chicken. ₅₈

Akin to the concept of critical risk is proportional deterrence. In this case, a potential opponent tries to determine the adversary's level of pain sufficient to deter by calculating the value of what is threatened. This is an important distinction in cases below MAD. Contrary to universal deterrence, purported to function when all states make nuclear threats in order to create systemic stability, specific losses are predicted, such as population, domestic political support of high leadership, long-term effects on the economy, and so forth. ₅₉ For example, does Saddam Hussein place a higher value on his own life and personal power than the survival of significant percentages of his population? Would the relatively moderate Khatami regime of Iran back down more readily to threats made to civilian centers? Most important, how would these dynamics affect a stance of nuclear deterrence, and how does Classical Deterrence Theory help discern these nuances?

With little regard to nuclear capability, purists of the Decision-Theoretic Deterrence Theory school reach their own logical conclusion — the belief that the simple existence of deployable nuclear weapons is sufficient to deter. ₆₀ In other words, inanimate weapons should "create their own logic". ₆₁ How, than, does one describe a decision-maker that does not follow the same logic? The tendency has been to label them as 'irrational' or 'crazy'. ₆₂ Risking nuclear use, even at the levels experienced at Hiroshima and Nagasaki, does not automatically appear to be a sane option. Yet, repeatedly in history, we have seen actors make conscious decisions and take steps that have resulted in extreme suffering. According to Thucydides, the Melians refused to join the Athenian alliance, fully aware that their men would be slaughtered and boys castrated to join their women in a life of slavery. Was this account simply a parable to stress the moral dimension of power in international relations, or a chapter of history akin to Masada that would, and still can, repeat itself? Let us also consider a more Machiavellian leadership, such as a Saddam Hussein that would commit heinous acts against his own Kurdish population or submit his population to debilitating sanctions while maintaining a palatial lifestyle for himself? ₆₃ In either kind of situation, one aspect is always the same. To assume that any level of nuclear possession automatically will preclude nuclear use is foolhardy, particularly when a state is basing its security policies on this assumption.

Automatically equating nuclear risk-taking with irrational decision-making is not possible at all levels of nuclear capability. It is of the highest relevance to recognize that policy considerations geared toward preventing nuclear use could omit potential solutions. The likelihood of additional horizontal and vertical proliferation based on a 'balance of terror' can even increase. Scholars who support this path are in the minority, yet alternatives have yet to be based upon a solid foundation of deterrence theory. The fact that nuclear deterrence theory was developed in one kind of world does not mean that it cannot be instructive in others, if properly applied. By considering a state's level of nuclear capability as an independent variable with multiple variations, the causal effects on crisis behavior can be more accurately assessed and tested. In this manner, other policies, such as those that promote confidence building measures or other kinds of security assurances, can be identified and put forward with increased confidence. In illustration, the next section offers a brief description of a dyad with a capability furthest removed from the Cold War superpowers — the mini-arsenal states of Iran and Iraq. This is followed by a potential, and more discerning, coding of nuclear capability with a sample application.

 

III. Mini-Arsenal Dyads: Iran and Iraq ₆₄

The history of the Cold War is exemplified by the U.S. policy of nuclear deterrence. The lessons from that period of super-arsenal contest continue to influence policy toward other states. Today, however, targets include states below super-arsenal capability, including the quasi-nuclear states of Iran and Iraq. Therefore, there may be considerable misdirected efforts that may not only fail to meet the objective of removing nuclear use as a crisis option, but actually increasing the likelihood.

Iraq's nuclear progress has been well known since the aftermath of Desert Storm. Its nuclear proliferation program has been severely hindered, but much of the human talent remains, and possibility significant material components of the proliferation attempt that have not been discovered by inspectors. If allowed, Iraq may quickly proliferate once sanctions are lifted. ₆₅

Iran's current effort to proliferate originally began under the Shah. While Iran denies any attempt to acquire a nuclear force structure, evidence points to the contrary. IAEA inspections are conducted on a regular basis, but these only take place at declared sites with declared nuclear materials. ₆₆ It is possible, therefore, that Iran is trying to proliferate. Iran is energy-rich. Due to cost of creating a nuclear energy program, using its existing electrical power based on natural gas would be less than 10% of the cost nuclear generated power. However, Iran's current goal to provide as much as 20% of its energy from nuclear power plants. Iranian nuclear-related acquisitions also are suspect. The evidence indicates that Iran's true intent is to gain the ability to build its own nuclear warheads. ₆₇ As early as 1993, Iran and a sanction-free Iraq were predicted to be able to produce one to three fission bombs by this time. ₆₈

Iran and Iraq are well-suited to this kind of study since they gave been engaged in a protracted conflict. Protracted conflict, or "hostile interactions which extend over long periods of time with sporadic outbreaks of open warfare fluctuating in frequency and intensity", ₆₉ can be based on a number of factors. Protracted conflicts are not unique to the Middle East, ₇₀ yet due to a variety of ingredients, such as geographical proximity and border disputes, there have been many sparks over time. Therefore, there are multiple pre-war crises to study, as well as intra-war crises, between Iran and Iraq.

There also is a demographic, or ethnic, ingredient. Contrary to many ethnic-based conflicts in which the two sides can be defined and separated, the antagonism in this case is caused by a heterogeneous Iraqi society and cross-border affinities with Iran. Iran is predominantly Persian, with 24% Azerbaijani and a sprinkling of other groups. However, 89% of the population adheres to the Shi'a sect of Islam. Iraq, on the other hand, has a much more diverse population. The current leadership is Arab Sunni, a segment of society that only comprises 20% of Iraqis. The majority of the remaining Sunnis are Kurds, who have been persecuted by Hussein's government. Over 60% of the population as a whole are Arab Shi'a. With strong cross-border religious ties, Baghdad often perceives Iran as a challenge for the loyalty of many Iraqis.

Both Iran and Iraq, even if they gain the ability to build (or buy) a nuclear weapons capability, would be likely to remain at the level of a mini-arsenal for a duration of time that could experience multiple crises. Since mini-arsenals may not be able to guarantee nuclear escalation to unacceptable levels, they may appear to be a viable military or political option, a potential weakness to a deterrent stance. This is particularly true if an emphasis on military advantage overcomes a fear of physical damage. ₇₁

Efforts to prevent proliferation in the Northern Tier have been of up-most importance to the NPR, with the United States leading the charge. Prior to the 1980s, the US sought to control Iran and Iraq by encouraging a regional balance of power. Assisting one state, and then the other, this process came to halt with the 1979 Iranian Revolution and failure of the United States to achieve an open dialogue with the new government. Since that time, a series of laws have been passed in an attempt to continue exerting influence in the region. On October 23, 1992, President Bush signed into law the Iran-Iraq Non-Proliferation Act, promising sanctions on nuclear suppliers. The Clinton Administration began by following a policy of 'dual containment', ₇₂ hoping to strangle any nuclear weapons program until governments friendly, or at least malleable to the US, came to power. ₇₃ The Iran-Lybia Sanctions Act was added in 1996, penalizing foreign companies investing $20 million or more in either state's energy industry. Relations with Iran have warmed a bit, but the US still believes that Teheran covets nuclear weapons, as well as long-range missiles. ₇₄ Overall, however, many US policies have been ineffectual due to lack of support from other states. Proof of this is 'counterproliferation', a policy that recognizes proliferation can occur and seeks to provide protection from nuclear-armed adversaries. ₇₅ In contrast, NPR's successes are typically multilateral in nature.

In sum, two states within a protracted conflict wish to acquire nuclear force structures but are inhibited, and therefore restricted, to a mini-arsenal potential. The policies geared toward preventing nuclear use in the Northern Tier do not address underlying motivations to acquire the bomb. Instead, they are maintaining a situation in which proliferation, however difficult, can occur. Classical Deterrence Theory, when considering rational actors at various levels of nuclear capability, may indicate that a nuclear-capable Iran and Iraq within a crisis may choose to use their nuclear weapons and risk retaliation. The next section provides one example of a game-theoretic approach to investigate potential nuclear use. If this tendency is detected, more effective policies need to be recommended than those based on traditional, Cold War nuclear deterrence.

 

IV. Theory of Moves and Nuclear Arsenal Games

While it has been assumed that nuclear dynamics between smaller powers will manifest the same underlying assumptions, theory and research rather than faith would seem more appropriate as a basis for beliefs when the consequences of error may be serious. Consider the recent example of the shock among policy community analysts over Indian and Pakistani nuclear testing. ₇₆ Did the Indo-Pakistani rivalry became more complicated and dangerous as a result of their breach of international norms against testing? Or did nuclear deterrence, a la the Cold War, become more robust and therefore offer the promise of greater crisis stability? Standard approaches based on the experiences of the superpowers with super-arsenals are unlikely to generate useful theory and policy for a rapidly changing situation that involves other kinds of arsenals.

The model provides the foundation for development of a multi-purpose data set. In this piece, the data, and the taxonomy and typologies derived from it, will be used to generate propositions based on the Nuclear Arsenal Games (NAG), adapted from the Theory of Moves, or TOM, a game-theoretic model. ₇₇ The purpose of this study, however, is not to make a contribution to the development of game theory or to debate the strengths and weaknesses of various existing approaches. Instead, TOM, is ideal for demonstrating the importance of creating a data base that indicates various types of WMD capabilities and related potential preferences. ₇₈ I have chosen TOM for the following positive traits it offers to a study with the present research objectives, which collectively outweigh the areas in which it seems less relevant: actors the ability to have a 'history' ₇₉ ; players move sequentially rather than simultaneously ₈₀ ; information and misinformation are reflected ₈₁ ; and TOM provides a framework capable of being expanded toward a more comprehensive model. ₈₂ Most important, TOM offers a game-theoretic model that is approachable to a variety of 'consumers', both academic and policy-oriented. Emulating this, the NAG intends to offer understanding and prediction to more than the minority of academics with advanced training in specialized game theory. ₈₃ The NAG, based on TOM, can be grasped in application by undergraduates, security experts of any background, practitioners and policymakers. In addition, the data set created for use in assessing propositions generated by the NAG is compatible with diverse methodological applications, from descriptive case studies to advanced quantitative analysis.

TOM addresses the following questions about crisis interactions:

1. Under what conditions will players move in a specified order?
2. When a player moves, what is its optimal strategy (i.e., where will it move)?
3. When players think ahead more than one step, would they act differently (say, by moving from a Nash equilibrium, or a state from which no player would have an incentive to depart unilaterally because its departure would immediately lead to a worse, or at least not better, state)?

The ability to answer the questions above in the context of a game between nuclear arsenal states under crisis conditions sums up the basic theoretical significance of this study. With respect to policy, this study goes beyond the bulk of prior analysis by discarding the implicit assumption that the logic of superpower rivalry and super-arsenals will be present in other nuclear-capable dyads as well. Results from analysis of the NAG in the crisis setting should provide insights into policy that would not be available from a strictly superpower-oriented frame of reference.

TOM begins play of a game by assuming that players are in a particular state or situation — at which they receive payoffs — and from which they can, by switching their strategies, attempt to move to a better state. The game is dynamic because the players start with a past, which determines the state where play begins. In this case, the players begin in a Cooperate/Cooperate state, meaning neither side has launched a first strike. (Recall that mutual cooperation does not infer peace or the absence of a crisis.) This reflects the present reality of all potential nuclear dyads save the US/Japan instance from 1945. (To date, Japan is not considered as a potential nuclear proliferator). Players then compare this situation with future states they and other players can create by moving one or more times. As they look ahead at their possible moves, the possible countermoves of other players, their own counter-countermoves, and so on, the players try to anticipate where a game will terminate, which is where they are assumed to obtain the best feasible payoffs.

Figure 2 shows the generic version of a 2x2 game. Each player has two strategies, s₁ and s₂ for Row, and t₁ and t₂ for Column. The alternative strategies are defined simply as non-use, or "Cooperate" (s₁ and t₁), and use, or "Defect" (s₂ and t₂) of the nuclear arsenal. The payoffs resulting from the outcomes are generated by each combination of strategies appear respectively for Row and Column in each cell of the matrix. The players in TOM begin at an initial state that reflects a previous outcome or point in time. Either player can begin the game by switching their strategy. Alternating responses continue until the player whose turn it is to move next chooses not to switch its strategy. When this happens the game ends, reaching its final state. ₈₄

When nuclear weapons enter the equation, standard game theory concentrates heavily exclusively on one set of preferences, referring to those of Chicken or first-level adversaries. Chicken would translate into r₃ > r₁ > r₂ > r₄ in Figure 2 (generic game) for Row and a symmetric preference ordering for Column. At the theoretical level, the point of departure for this analysis is an objection to the assumption that all nuclear rivalries, when manifested in crisis interactions, necessarily follow this logic. Three other types of players (i.e., preference orderings) are posited here, but more are possible. This brief description will not seek to explain the logic behind each preference ordering in any detail, but instead simply put the typology forward to see if it can help to explain the dynamics of nuclear crises. Next will be a sample hypothesis for one dyad, namely, that behavior consistent with some combinations of player types may be more likely than others to be observed, depending on the nuclear force structure of the participants.

For ease of exposition, Row's preferences will be presented in each instance to convey the possible types of players ( Table 2). These preferences, in accordance with TOM, are ordinal, rather than cardinal. In other words, they present the order of preferences, rather than the degree of preference. Type I holds the standard preferences from the game of Chicken as noted above: r₃ > r₁ > r₂ > r₄. This ordering reflects the basic unacceptability of a nuclear exchange; a victory is preferred but even defeat is better than a nuclear exchange. Type II preferences somewhat slightly from the standard version: r₃ > r₁ > r₄ > r₂ (Prisoners' Dilemma). ₈₅ Type III is even further removed from Chicken: r₃ > r₄ > r₁ > r₂. This preference ordering builds in rivalry to the extreme: a player would rather exchange nuclear weapons than remain in a position of mutual non-use. Row believes that it can survive a nuclear attack and is motivated to strike based on factors ranging from the perceived need to preempt (including the possibility of reducing or even preventing a retaliatory second strike) to concerns about reputation in future crises. ₈₆ Type IV, the utopia of proliferation optimists, represents the preferences of actors who would never use nuclear weapons; in a symmetric super-arsenal dyad neither actor would consider leaving mutual restraint or non-use: r₁ > r₃ > r₂ > r₄.

In this game, Iran and Iraq are both depicted at Type III preference states. These states fought each other in an eight-year war during the 1980s that quickly became a long, bloody war of attrition. Over one million people were killed and the cost rose to the hundreds of billions of dollars. The level of barbarity was exemplified by Iranian use of the "human wave" against fortified positions and intensive Iraqi bombings of Iranian population centers. ₈₇ Chemical weapons were used on both sides, plus Iraq used chemical weapons against its own Kurdish civilians. ₈₈ It still can be assumed that neither state has the military power to win a conventional war against the other decisively. The prospect, therefore, is another conflict extracting terrible demands on both societies without eliminating the protracted nature of Iranian-Iraqi animosity. It is feasible that to leadership, only defeat would be worse. The damage that might be sustained by two or three Hiroshima strength bombs might be considered a rational risk, especially if the military scales could be tipped toward a decisive advantage. Again, the game cane be played inserting any set of preferences, as might be appropriate if, for example, a decision-maker is receiving conflicting predictions from advisors.

Players of Types I-IV, of course, may exist in no place other than the imagination of the game theorist. However, it also is possible that these types — in varying combinations — have participated and will continue to be observed in real nuclear crises. In the abstract, considering these four examples, a total of 10 combinations of types exist (i.e., ordering does not matter, so (I, III) is the same as (III, I)). Recognizing limited time and space, it is beyond the scope of this project to enumerate propositions about all of the scenarios — matching the combinations of preferences with each of the four types of arsenals that may exist — so one example of a symmetric dyad will be provided as a starting point: a mini-arsenal pairing. If two states are believed to possess mini-arsenals, their history of crisis behavior, including non-nuclear crises, can be traced to learn what actions or reactions typified their behavior. Presented now is a sample proposal considering that behavior consistent with Type III preference orderings may be one expectation between Iran and Iraq.

The sample Type III hypothesis about crisis interactions between a symmetric dyad of mini-arsenal states follows:

Type III Symmetric Mini-Arsenal Hypothesis: Crisis interactions between mini-arsenal states should conform to dyads of state preferences expected from the following combinations of types of players, in descending order of probability: (III, III) > (II, III) > (II, II) > (I, I), (I, II), (I, III), (I, IV), (II, IV), (III, IV), (IV, IV).

All ten combinations of types of player preferences are listed. Analogous general hypotheses can be worked out for each of the other possible combinations. Note that crisis behavior in this particular mini-arsenal dyad is expected to be most similar to that manifested by a dyad composed of Type III players, with hybrids of II and III being less probable and any and all combinations involving Type I or IV players regarded as least likely. In other words, the hypothesis asserts that the sequence of moves in a crisis between these two mini-arsenal states and the outcome of the case are most likely to resemble what TOM would predict for a Type III dyad and less likely for other combinations.

The solution for one game matrix will be provided to show how TOM predicts the sequence of play and outcomes for each combination of players ( Figure 3). Assume that the players (NAG as applied to Iran and Iraq) are both Type III with a mini-arsenal capability. The preferences translate in the following states: (r₁,c₁) = (2,2), (r₂,c₂) = (1,4), (r₃,c₃) = (4,1) and (r₄,c₄) = (3,3). ₈₉

The initial state is assessed to be the upper-left cell, indicating that nuclear use, or defection, has not occurred. Since the game is symmetric it does not matter who starts the play, so let it be assumed that Row starts. TOM uses a method of "backward induction" to lay out countermoves and counter-countermoves, allowing each player to consider future ramifications of a potential move. ₉₀ Consider the following sequence of moves (or changes in strategy) by Row (R) and Column (C):

State 1	State 2	State 3	State 4	State 1
R Moves	C Moves	R Moves	C Moves
(2,2) ==>	(4,1) ==>	(3,3) ==>	(1,4) ==>	(2,2)

Assume that the players have moved counterclockwise as just noted above, from (2,2) though a complete cycle. It would be C's decision to move out of (1,4), the state with C's best playoff, in order to reach (2,2). According to TOM, no state would move from 4, its best outcome. This preference is noted by a vertical line, which indicates that C would not change strategies from (1,4) to (2,2).

Continuing backward, would R move from (3,3) to (1,4), R's worst payoff and C's best? Knowing that C would refuse to leave, a rational R therefore would remain at (3,3), also indicated by a vertical line. Now C must consider a move from (4,1), its worst state, to (3,3), realizing that a rational R will have no reason to leave the latter state. This move makes sense for C. So, at the initial state of (2,2), R is faced with the decision of whether to move to (4,1), its best state, with the expectation that the game then would progress to (3,3) and end there.

To summarize the play, backward induction causes R to look ahead and see that it would prefer not to move beyond (3,3) in the sequence, making this the final state. It is the predicted outcome, the nonmyopic equilibrium, or the state from which neither player, considering all subsequent moves and countermoves, will have an incentive to depart from unilaterally. Any other possible final states would be worse, or at least not better. ₉₁ The players, therefore, end up at (3,3), meaning a nuclear exchange. This is a very disturbing result. In this situation, the pressure toward preemption in this situation faced by Iran and Iraq, to cite one example, is enormous.

This example shows what TOM has to offer in terms of further analysis of a game such as the Type III/III variant for which its initial predicted outcome is no different from standard game theory. Brams develops auxiliary concepts, such as order and threat power, that can help to assess the prospects for moving players away from the initially predicted outcome. ₉₂ Threat power, for example, refers to the ability of a player to "threaten the other with the possibility of a Pareto-inferior state [i.e., there exists a state that is better for all or at least one and not worse for the others] — without necessarily moving there — by communicating its intentions in advance". ₉₃

 

V. Conclusion

TOM, as applied to states with mini-arsenal preferences, suggests a frightening propensity toward a nuclear exchange. ₉₄ At first glance this kind of scenario appears quite pessimistic, particularly if the actors are depicted as 'crazy', 'pariah', 'rogue' or 'backlash' states. ₉₅ Yet this need not be the case. Policies can be tailored to alter the preferences of rational actors, even if the value systems attributed to these antagonists might appear reprehensible. Alternate preferences would change the game and, consequently, its results. So it is worth pursuing more creative policies than those in force, such as dual containment and counterproliferation, which would seem to have little or no chance to change the preferences just described.

Chicken and Prisoners' Dilemma (when played according to TOM, beginning at mutual cooperation or non-use) can reach stable, non-use outcomes. Is it possible to alter player preferences to reflect one of these games? NPR operates under the premise that by substituting the perceived need to proliferate, states will not suffer the international condemnation and national risk by doing so. Perhaps preventing proliferated states from initiating nuclear use can be approached in the same manner, providing substitutes for perceived advantages associated with first use.

One possibility would be to allow Iran and Iraq to fulfill their security needs at the conventional level. Theoretically, if either believes it can meet national objectives without first-use, there would be little logic in risking a second strike. As mentioned above, another option some scholars advocate is a safe, assisted increase in nuclear capability to reach the level of destructive potential required to reach unacceptable damage and stable deterrence.

Regional answers may make more sense. Mimicking South America, the major powers in the Middle East could forswear nuclear arsenal development programs. This option, of course, centers around Israel, since it is a known, although not declared, nuclear state. Security umbrellas over regional actors could provide sufficient substitutions for security needs. Interallied control, such as NATO implements in keeping Turkey and Greece at bay, also could serve to increase the costs of certain kinds of aggressive military action between states without forcing disarmament.

Alternative energy options, as opposed to sanctions, may help with the basic problem entailed by dual-use technologies: the ability to convert nuclear energy programs to weapons capability. In other words, it may be better to seek indirect control over the growth of arsenals. The technology already exists to build nuclear energy reactors that do not produce weapons-grade fissile material as a byproduct. Under-utilized sources of energy could be developed further. For example, Iran has considerable natural gas resources and Iraq a greater potential for hydroelectric power than it currently operates.

The final goal of any of these policy prescriptions is to place Iranian and Iraqi state leadership in a strategic situation that reorders their preferences from a dangerous game, such as the Type III-III NAG, in which a nuclear exchange is preferred to conventional war, into a game that leans toward mutual non-use as a stable, final result. Classical, or 'Rational', Deterrence Theory still can be instructive in reaching this end. Deterrence strategies based on distribution of power and potential costs remain a consideration as the basis for preventing war, including nuclear war. This study presents a model, based on TOM, for systematically testing what levels of cost are sufficient for a rational actor to be deterred, emphasizing the need to consider specific states and their behavior in crises. Viewed as rational actors, but recognizing the impact of various nuclear capabilities (including the most limited) states such as Iran and Iraq can be approached directly with policies aimed toward their functional incorporation into the mainstream of the international system.

 

Table 1: Levels of Nuclear Force Capabilities  (Back)

Levels	Warhead Capability	Destructive Capacity	States
(First) Super-Arsenals	Several 100s or 1000s	Second-Strike Assured Destruction at a Global Level	United States (7200)* Russia (5972)
Second	100s	Second-Strike Assured Destruction at a Dyadic Level	China (400) France (450) United Kingdom (250)
Third	Dozens	Second-Strike Assured Destruction of State But Not Society	Pakistan (12)** India (50)** Israel (100) ***
(Fourth) Mini-Arsenals	Two to Three Crude Hiroshima-Style Bombs	No Second Strike Assured Destruction of State or Society	Iran, Iraq, Syria, Lybia, North Korea****

* All the numbers here are for stockpiled, rather than strictly operational and/or strategic weapons. The model will consider these as well as other important factors in determining total force structures. Due to security factors, obtaining numbers with certainty is usually impossible. However, several indicators are available that can be used to make estimates of the highest quality. As noted above with India vis-à-vis Pakistan and China, during a specific crisis with a particular opponent, a state may be placed at a different level of destructive capacity.

** These are numbers of weapons possible, considering the materials in possession.

*** Some sources speculate Israel's 'opaque' arsenal to be as large as 100 operational warheads, while others run higher. Israel's nuclear 'opacity' has recently been challenged in the Knesset. Nina Gilbert, "Hadash MK's Debate of Israeli Nuclear Policies Stirs Knesset Storm," Jerusalem Post (February 3, 2000), and Nina Gilbert, "Vanunu Documents to be Debated in Knesset," Jerusalem Post (January 19, 2000).

**** Mini-arsenal states include states at this level of capability as well as those about to achieve it. States restricted to this level of capability historically have pursued their nuclear weapons programs covertly. In other words, it may be difficult to impossible to detect when practical proliferation, or operational status, actually occurs, particularly at these minimum levels.

 

Table 2: State Types According to Nuclear Preferences  (Back)

State Types	Nuclear Preferences
Type I	4 — unilateral attack against enemy without nuclear retaliation* 3 — mutual nuclear restraint 2 — unilateral attack by enemy without nuclear response 1 — mutual nuclear use
Type II	4 — unilateral attack against enemy without nuclear retaliation 3 — mutual nuclear restraint 2 — mutual nuclear use 1 — unilateral attack by enemy without nuclear response
Type III	4 — unilateral attack against the enemy without nuclear retaliation 3 — mutual nuclear use 2 — mutual nuclear restraint 1 — unilateral attack by the enemy without nuclear response
Type IV**	4 — mutual nuclear restraint 3 — unilateral attack against the enemy without nuclear response 2 — unilateral attack by the enemy without nuclear retaliation 1 — mutual nuclear use

* Unilateral use, without second strike, has been questioned on both moral and strategic terms. However, Cold War MAD was based on the credibility of nuclear first use.

** There are many more possible Types, at least in the abstract. As research on the NAG progresses and the data is assembled and used in testing, those types that reflect behavior in actual crises will be determined.

 

Figure 1: The Weapon Plane  (Back)

Source: Intriligator and Brito, "Can Arms Races Lead to the Outbreak of War?", 77.

 

Figure 2: Generic 2x2 Matrix*  (Back)

		Column Player Strategies
		t1	t2
Row Player Strategies	s1	(r1,c1)	(r2,c2)
	s2	(r3,c3)	(r4,c4)

*Payoffs for each player are listed respectively within the cells of the matrix.

 

Figure 3: Type III-III NAG: Iran and Iraq  (Back)

		Iraq Strategies
		C—no nuclear use	D—nuclear use
Iran Strategies	C—no nuclear use	(2,2)	(1,4)
	D—nuclear use	(4,1)	(3,3)

 

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Endnotes

Note 1:  Michael Brecher and Jonathan Wilkenfeld, A Study of Crisis (Ann Arbor: University of Michigan Press, 1997), 4-5. This major work presents ICB data and research findings that have accumulated over the preceding two decades. Back.

Note 2:  Carolyn C. James, "Iran and Iraq as Rational Crisis Actors: Dangers and Dynamics of Survivable Nuclear War," Journal of Strategic Studies 23/1 (2000). Back.

Note 3:  Pierre Gallois, The Balance of Terror: Strategy for the Nuclear Age, translated by Richard Howard, (Boston: Houghton-Mifflin, 1961); and Albert Wohlstetter, "The Delicate Balance of Terror," Foreign Affairs 37 (1959), 211-34. Back.

Note 4:  Since many of the most primitive states have acquired sophisticated delivery technology, and even the most primitive methods of delivery can be effective with weaponry as destructive as nuclear warheads, the concentration here is on the size of the arsenals rather than comparing delivery systems. Steven R. David, "Why the Third World Still Matters," International Security 17/3 (1992), 127-159; and Lewis A. Dunn, "New Nuclear Threats to US Security." in Robert D. Blackwill and Albert Carnesale, eds., New Nuclear Nations: Consequences for US Policy (New York: Council on Foreign Relations Press, 1993). Thus, the assumption is that crisis behavior is influenced primarily by the arsenal itself rather than integrated weapons systems.  Back.

Note 5:  James, "Iran and Iraq as Rational Crisis Actors". Back.

Note 6:  The idea that a nuclear attack may be survivable can lead to thinking akin to Wirtz's concept of 'conventionalization', in which nuclear weapons are given the attributes of conventional weapons rather than being treated as a revolutionary development. This is most likely to occur at force levels less than MAD. James J. Wirtz, "Counterproliferation, Conventional Counterforce and Nuclear War," Journal of Strategic Studies 23/1 (2000). A military edge also may be sufficient to justify a limited nuclear attack if defeat of the enemy is deemed possible. Lawrence Freedman, "I Exist; Therefore I Deter," International Security 13/1 (1988), 177-195. Back.

Note 7:  The United States had a strategic nuclear force capability from 1945. In this early period, both states relied exclusively on long-range bombers. By the end of 1949, the USSR had one non-strategic warhead. It was not until 1956 that the Soviet Union possessed strategic warheads, estimated at 126. The US and USSR acquired operational ICBM forces in 1959 and 1960, respectively, and SLBMs in 1960 and 1958, respectively. Robert S. Norris and William M. Arkin US and USSR/Russian Strategic Offensive Nuclear Forces, 1945-1996 (Washington, D.C.: Natural Resources Defense Council, 1997).  Back.

Note 8:  Bernard Brodie, From Crossbow to H-Bomb (Bloomington: Indiana University Press, 1973); Robert Jervis, Perception and Misperception in International Politics (Princeton: Princeton University Press, 1976); Klaus Knorr, On the Use of Military Power in the Nuclear Age (Princeton: Princeton University Press, 1966); Thomas C. Schelling, Arms and Influence (New Haven: Yale University Press, 1966); and Wohlstetter, "The Delicate Balance of Terror". Back.

Note 9:  In 1962, the United States is estimated to have possessed an offensive force loading capability of 1653 strategic launchers and 3451 warheads. The Soviet Union are believed to have had 276 strategic launchers and 497 warheads. The numbers for launchers in inventory and stockpiled weapons runs much higher. Norris and Arkin, US and USSR/Russian Strategic Offensive Nuclear Forces. Back.

Note 10:  Bernard Brodie, The Absolute Weapon: Atomic Power and World Order (NY: Harcourt, Brace and Company, 1946); Bernard Brodie, Strategy in the Missile Age (Princeton: Princeton University Press, 1965); Bernard Brodie, War and Politics (New York: Macmillan, 1973); Stephen J. Cimbala, Nuclear Strategizing: Deterrence and Reality (New York: Praeger, 1988); Alexander L. George and Richard Smoke, Deterrence in American Foreign Policy: Theory and Practice (New York: Columbia University Press, 1974); Frank Harvey, "Rigor Mortis, or Rigor, More Tests: Necessity, Sufficiency, and Deterrence Logic," International Studies Quarterly 42 (1998), 675-707; and Herman Kahn, On Escalation: Metaphors and Scenarios (New York: Frederick A. Praeger, Publishers, 1965). Back.

Note 11:  Schelling, Arms and Influence, 116-125; and Glenn H. Snyder & Paul Deising, Conflict Among Nations (Princeton, NJ: Princeton University Press, 1977), 107-122. Back.

Note 12:  Even critics of rational deterrence generally rely on Cold War, super-arsenal examples. See, for example, Richard Ned Lebow and Janice Gross Stein, "Deterrence and the Cold War," Political Science Quarterly 110/2 (1995). While there is not an inherent problem in using the US/Soviet example, this paper argues that a comprehensive study of nuclear deterrence requires evidence from states at all nuclear levels. Back.

Note 13:  'Rational' is defined in this paper according to Morgan's discussion of deterrence under rational decision-making: "What is 'rational' action varies with one's goals and resources; what does not vary is the process itself: specifying and ordering objectives, defining the particular situation, gathering relevant information on alternatives, and choosing the alternative that maximizes one's welfare." Patrick M. Morgan, Deterrence: A Conceptual Analysis (Beverly Hills: Sage Publications, 1983), 84. Back.

Note 14:  Perceptions about nuclear deterrence and rational decision-making also can play a role in a state's initial drive to proliferation.  Back.

Note 15:  The CIA reported in December 1999 that the agency could no longer claim with any assurance that Iran does not already have a bomb, although presently there is no firm proof to that effect. James Risen and Judith Miller, "CIA Tells Clinton an Iranian Bomb Can't Be Ruled Out," New York Times (January 17, 2000). Back.

Note 16:  An assessment for proper identification of rivalries using time series data can be found in Erik Gartzke and Michael W. Simon, "'Hot Hand': A Critical Analysis of Enduring Rivalries" Journal of Politics 61/3 (1999), 777-798. Back.

Note 17:  I will be referring only to nuclear, rather than conventional, deterrence. This paper also does not cover similar phenomena associated with biological and chemical weapons of mass destruction. However, research into these realms is a recommended extension of NAG. Back.

Note 18:  Robert Jervis, "Deterrence Theory Revisited," World Politics 31/3 (1979), 289-324:289. Back.

Note 19:  Schelling, Thomas C., The Strategy of Conflict (New York: Twentieth Century Fund, 1960), 187-203. Back.

Note 20:  The premise is stated here in a simple manner. Translating nuclear weapons into state power, of course, can require recognizing multiple nuances and problems. T.V. Paul, "Power, Influence, and Nuclear Weapons: A Reassessment," in The Absolute Weapon Revisited, in T.V. Paul, Richard J. Harknett and James J. Wirtz, eds., (Ann Arbor: University of Michigan Press, 1998). A common expectation of nuclear capability is a lower probability of escalation when conventional forces are balanced. Paul Huth, C. Gelpi and D. Scott Bennett, "The Escalation of Great Power Militarized Disputes: Testing Rational Deterrence Theory and Structural Realism," American Political Science Review 87/3, 609-623. Back.

Note 21:  Edward Rhodes, Power and Madness: The Logic of Nuclear Coercion/ (New York: Columbia University Press, 1989), 143. Back.

Note 22:  Ibid., 137-140. Consensus that nuclear weapons have a special deterrent effect on non-nuclear opponents during a crisis does not exist. See Jacek Kugler, "Terror Without Deterrence: the Role of Nuclear Weapons," Journal of Conflict Resolution 28/3 (1984), 451-469; and Daniel S. Geller, "Nuclear Weapons, Deterrence, and Crisis Escalation," Journal of Conflict Resolution 34/2 (1990), 291-310. Back.

Note 23:  Morgan, Deterrence; and Frank C. Zagare, "A Stability Analysis of the U.S.- USSR Strategic Relatioship," In Frank C. Zagare and Jacek Kugler, eds., Exploring the Stability of Deterrence (Boulder: Lynne Rienner, 1987). Back.

Note 24:  Zagare, "A Stability Analysis of the U.S.- USSR Strategic Relationship," 124-131. Back.

Note 25:  Brams depicts the second worst outcome in Chicken as caving into an opponent's demands, or defeat, not a unilateral exchange. Steven J. Brams, Superpower Games: Applying Game Theory to Superpower Conflict (New Haven: Yale University Press, 1985), 9-13. Back.

Note 26:  Schelling, Arms and Influence, 36-43. Back.

Note 27:   Jervis, "Deterrence Theory Revisited", 299-301. Back.

Note 28:  Brodie, The Absolute Weapon. Back.

Note 29:  McGeorge Bundy, "The Bishops and the Bomb," The New York Review of Books 30/10 (June 16, 1983); and McGeorge Bundy, "Existential Deterrence and its Consequences," in Douglas MacLean, ed., The Security Gamble: Deterrence Dilemmas in the Nuclear Age (Totowa, N.J.: Rowman and Allanheld, 1984). Back.

Note 30:  Devin T. Hagerty, "Nuclear Deterrence in South Asia: The 1990 Indo-Pakistani Crisis," International Security 20/3 (1995), 79-114; David J. Karl, "Proliferation Pessimism and Emerging Nuclear Powers," International Security 21/3 (1996), 87-199; John J. Mearsheimer, "The Case for a Ukrainian Nuclear Deterrent," Foreign Affairs 72/3 (1993), 50-66; Jordan Seng, "Less Is More: Command and Control Advantages of Emerging Nuclear Nations," Security Studies 6/4 (1997), 50-92; Kenneth N. Waltz, The Spread of Nuclear Weapons: More May Be Better (Adelphi Paper 71, London: International Institute for Strategic Studies, 1981); Kenneth N. Waltz, "More May Be Better" and "Waltz Responds to Sagan," in Scott D. Sagan and Kenneth N. Waltz, eds., The Spread of Nuclear Weapons: A Debate (New York: W. W. Norton & Company, 1995). Back.

Note 31:  Bruce B. Blair, The Logic of Accidental Nuclear War (Washington, D.C.: Brookings Institution, 1993); Peter D. Feaver, Guarding the Guardians: Civilian Control of Nuclear Weapons in the United States (Ithaca: Cornell University Press, 1992); Peter D. Feaver, "Command and Control in Emerging Nuclear States" International Security 17/3 (1992), 160-187; Scott D. Sagan, The Limits of Safety: Organizations, Accidents and Nuclear Weapons (Princeton: Princeton University Press, 1993); and Scott D. Sagan, "More Will Be Worse" and "Sagan Responds to Waltz," in Scott D. Sagan and Kenneth N. Waltz, eds., The Spread of Nuclear Weapons: A Debate (New York: W. W. Norton & Company, 1995). Back.

Note 32:  Richard Smoke, War: Controlling Escalation (Cambridge, MA: Harvard University Press, 1977), 17. Back.

Note 33:  Other uses of the term escalation can refer to a crisis moving from an embryonic stage to a full-scale crisis, from non-violence to the use of force, and an increase in violence from low to high levels without distinguishing conventional from non-conventional weapons. Michael Brecher, Crises in World Politics: Theory and Reality (Oxford: Pergamon Pressm, 1993), 130. Back.

Note 34:  Kahn, On Escalation, 37-51. Back.

Note 35:  Ibid., 38-39. Back.

Note 36:  Ibid., 44. Back.

Note 37:  T.V. Paul, "Nuclear Taboo and War Initiation in Regional Conflicts," Journal of Conflict Resolution 39/4 (1995), 696-717. Back.

Note 38:  Lawrence Freedman, The Evolution of Nuclear Strategy (London: St. Martin's Press, 1989), 217-219. Back.

Note 39:  Kenneth N. Waltz, "More May Be Better," 20-21. Back.

Note 40:  Kenneth N. Waltz, "Waltz Responds to Sagan,", 108-109. Back.

Note 41:  Scott D. Sagan, "More Will Be Worse". Back.

Note 42:  David Alan Rosenberg, "The Origins of Overkill: Nuclear Weapons and American Strategy, 1945-1960," International Security 7/4 (1983), 3-65. Back.

Note 43:  Graham R. Allison, Albert Carnesale and Joseph S. Nye, Jr., Hawks, Doves, and Owls: An Agenda For Avoiding Nuclear War (New York: W. W. Norton, 1984), 206-222. Back.

Note 44:  Jervis, "Deterrence Theory Revisited", 300. Back.

Note 45:  The political psychology school criticizes the rationality requirement for successful deterrence based on human limitations. Particularly in a crisis situation, people experience a variety of impediments to 'rational' decision-making, such as cognitive limitations, bureaucratic obstacles and cognitive bias. For an excellent review of this literature and its relation to rational choice theory, see Frank P. Harvey, "Rational Deterrence Theory Revisited: A Progress Report," Canadian Journal of Political Science 28/3 (1995), 403-435, and Frank Harvey, The Future's Back: Nuclear Rivalry, Deterrence Theory and Crisis Stability After the Cold War (Kingston and Montreal: McGill-Queen's University Press:1997), 6-17. Back.

Note 46:  Frank Zagare, "Classical Deterrence Theory: A Critical Assessment," International Interactions 21/4 (1996), 365-387. Back.

Note 47:  Michael D. Intriligator and Dagobert L. Brito, "The Stability of Mutual Deterrence," in Jacek Kugler and Frank C. Zagare, eds., Exploring the Stability of Deterrence Denver: Lynne Reinner, 1987); Morton Kaplan, System and Process in International Politics (New York: John Wiley, 1957); John J. Mearsheimer, "Back to the Future: Instability in Europe After the Cold War," International Security 15 (1990), 5-56; and Kenneth N. Waltz, Theory of International Politics (Reading, MA: Addison-Wesley, 1979). Back.

Note 48:  John Lewis Gaddis, The Long Peace: Inquiries Into the History of the Cold War (New York: Oxford University Press, 1987); and Kenneth N. Waltz, "The Emerging Structure of International Politics," International Security 18 (1993), 44-79. Back.

Note 49:  Zagare, "Classical Deterrence Theory," 368. Back.

Note 50:  Michael D. Intriligator and Dagobert L. Brito, "Can Arms Races Lead to the Outbreak of War?" Journal of Conflict Resolution 28 (1984), 63-84; and Intriligator and Brito, "The Stability of Nuclear Deterrence." Back.

Note 51:  Stein uses the term "norms of competition" to denote a situation in which adversaries share a tacit agreement of what is, for example, acceptable use of force. Janice Gross Stein, "Reassurance in International Conflict Managemen," Political Science Quarterly 106/3 (1991), 157-181. Back.

Note 52:  Waltz, The Spread of Nuclear Weapons. Back.

Note 53:  Bruce Bueno de Mesquita, and William H. Riker, "An Assessment of the Merits of Selective Nuclear Proliferation," Journal of Conflict Resolution 26/2 (1982); Peter Feaver and Emerson M. S. Niou, "Managing Nuclear Proliferation: Condemn, Strike or Assist?" International Studies Quarterly 40 (1996), 209-33; Mearsheimer, "The Case for a Ukrainian Nuclear Deterrent"; and Steven J. Rosen, "A Stable System of Mutual Nuclear Deterrence in the Arab-Isreali Conflict," American Political Science Review 71/4 (1977), 1367-1383. Back.

Note 54:  Zagare, "Classical Deterrence Theory," 383:fn. 10. Back.

Note 55:  Daniel Ellsberg, "The Theory and Practice of Blackmail," in Oran R. Young, ed., Bargaining: Formal Theories of Negotiation (Urbana, IL: University of Illinois Press, 1975). Back.

Note 56:  Glenn H. Snyder, "Crisis Bargaining," in Charles F. Hermann, ed., International Crises: Insights from Behavioral Research (New York: Free Press 1972). Back.

Note 57:  Ellsberg, "The Theory and Practice of Blackmail," 360; and Robert Jervis, "Bargaining and Bargainings Tactics," in J. Roland Pennock and John W. Chapman, eds., Coercion (Chicago: Aldine, 1972), 285. Back.

Note 58:  Herman Kahn, Thinking About the Unthinkable (New York: Horizon Press, 1962), 11. Back.

Note 59:  Gallois, The Balance of Terror. Back.

Note 60:  Bundy, "The Bishops and the Bomb"; Robert Jervis, The Illogic of American Nuclear Strategy (Ithaca: Cornell University Press, 1984); and Waltz, "The Emerging Structure of International Politics," 54. Back.

Note 61:  Zagare, "Classical Deterrence Theory," 379. Back.

Note 62:  Yehezkel, Dror, Crazy States: A Counterconventional Strategic Problem (Lexington, MA: Heath Lexington Books, 1971). Back.

Note 63:  UN Assistant Secretary General Denis Halliday, former UN coordinator in Iraq, resigned his post in 1998 in protest over the nature of sanctions against Iraq. Criticism exists among political actors and academics alike that the sanctions' primary intent has been to oust Saddam Hussein from power rather than influence Iraqi weapons of mass destruction policies. Halliday resigned due to his belief that the sanctions would not force disarmament. Rather, they had been responsible for malnutrition among 1/3 of Iraqi children under the age of 5 and in the deaths of 6-7000 children per month by the time Haliday left office. Phyllis Bennis, "The US and Iraq: towards confrontation?," Middle East International 587 (13 November 1998), 4-5; Ian Williams, "'Why I resigned' — an interview with Denis Halliday," Middle East International 587 (13 November 1998), 6-7.  Back.

Note 64:  For an expanded discussion of this topic, see James, "Iran and Iraq as Rational Crisis Actors". Back.

Note 65:  Anthony H. Cordesman, U.S. Forces in the Middle East: Resources and Capabilities (Boulder: Westview Press, 1997); and Leonard S. Spector, "Can Proliferation Be Stopped? A Look at Events and Decisions in the mid-1990s" in Barry R. Schneider and William L. Dowdy, eds., Pulling Back From the Brink: Reducing and Countering Nuclear Threats (London: Frank Cass, 1998). Back.

Note 66:  Cordesman, ibid. Back.

Note 67:  Shahram Chubin, Iran's National Security Policy: Capabilities, Intentions & Impact (Washington D.C.: The Carnegie Endowment for International Peace, 1994), 50-55; Patrick Clawson, Iran's Challenge to the West: How, When & Why (Washington, D.C.: The Washington Institute for Near East Policy, 1993), 59-66; Anthony H. Cordesman, (1994) Iran & Iraq: The Threat from the Northern Gulf (Boulder: Westview, 1994), 105-107; and Anthony H. Cordesman, U.S. Forces in the Middle East. Back.

Note 68:  Dunn, "New Nuclear Threats to U.S. Security." See also footnote 15. Back.

Note 69:  Edward E. Azar, Paul Jureidini and Ronald McLaurin, "Protracted Social Conflict:Theory and Practice in the Middle East," Journal of Conflict Resolution 32/3 (1988), 41-60. Back.

Note 70:  Brecher and Wilkenfeld, A Study of Crisis, 5-6. Back.

Note 71:  Eric Herring, Danger and Opportunity: Explaining International Crisis Outcomes (Manchester: Manchester University Press, 1995). Back.

Note 72:  Martin Indyk, "Special Report: Clinton Administration Policy toward the Middle East," Washington Institute for Near East Policy Policywatch 84 (May 21, 1993), 5. Back.

Note 73:  R. Jeffrey Smith and Daniel Williams, "White House to Step Up Plans to Isolate Iran, Iraq," The Washington Post (May 23, 1993). Back.

Note 74:  Madeleine Albright. "Remarks at the Asia Society Dinner, June 17," As released by the Office of the Spokesman, US Department of State (June 18, 1998); William Cohen, "Threat Posed to America by WMD," US Department of Defense News Briefing (March 17, 1998); James P. Rubin, "US Department of State Daily Press Briefing" (June 18, 1998); and U. S. Government White Paper, "Iraq Weapons of Mass Destruction Programs." Washington, D.C. (February 13, 1998). Back.

Note 75:  James J. Wirtz, "Beyond Bipolarity: Prospects for Nuclear Stability after the Cold War." In T.V. Paul, Richard J. Harknett and James J. Wirtz, eds., The Absolute Weapon Revisited: Nuclear Arms and the Emerging International Order (Ann Arbor: University of Michigan Press, 1998). Back.

Note 76:  David Albright, "The Shots Heard 'Round the World'", Bulletin of the Atomic Scientists 54/4 (1998), 20-25. Back.

Note 77:  Steven J. Brams, Theory of Moves (Cambridge: Cambridge University Press, 1994). Back.

Note 78:  In comparison to other forms of game-theoretic models, it has many strengths for applied research, so it seems appropriate to begin by noting a few weaknesses. According to reviews in the American Political Science Review, Journal of Politics and Behavioral Science, TOM does not have certain qualities offered by more complex extensive form games, such as time and time preferences with discounting. These factors are studied more easily using cardinal preferences rather than TOM's ordinal preferences. In general, however, TOM has been seen as a viable alternative form of game theory in its ability to analyze crisis behavior. Scott Sigmund Gartner "Theory of Moves" (book review) Behavior Science 39-40 (1994), 338-339; and Gerald L. Sorokin, "Theory of Moves" (book review) Journal of Politics 57(1995), 1194-1195. Back.

Note 79:  In other words, the game starts at a point determined by actual past crises and present conditions. For example, only the United States has used nuclear weapons, and even then only against Japan. When considering potential nuclear use, any other pairing of actors today would begin at a position of mutual nuclear non-use. The research subsequently can be extended to chemical and biological weapons. In these instances, states such as Iraq will be considered in terms of its past use. Back.

Note 80:  Again, this reflects actual crisis situations in which a player both thinks ahead and reacts to its opponent. At times, a player may even move through a point at which there is lesser payoff, anticipating a better result in the long-run. This reflects the idea of a "Nonmyopic Equilibrium" (NME), which seems highly relevant to real crisis interactions. Brams, Theory of Moves; and Michael B. Nicholson "Theory of Moves" (book review), American Political Science Review 90/1-2 (1996), 169-170. Back.

Note 81:  Specifically, TOM can show results of a crisis in which one or more players misinterprets the particular game being played. Applied to the NAG, this allows a policymaker to consider conflicting information from advisors, identify the most unstable or dangerous predictions, and attempt to move toward stability (or non-use of nuclear weapons). Back.

Note 82:  As a result, the NAG's potential can include more than just nuclear dyads. Multiple actors within a single crisis can be considered, as well as combinations of WMD. Any number of actors and diverse capabilities, as well as concurrent crises, ultimately can be accommodated. Again, this more accurately mirrors actual events. For example, a crisis between Pakistan and India certainly will concern China, which may become an active participant. When a given crisis occurs, these states may possess of variety of WMD at different levels. Back.

Note 83:  Indeed, the gulf between research communities evident in International Security versus Journal of Conflict Resolution requires no further explanation; the "flawed dichotomy" in methods applied to the study of nuclear weapons is one of the most glaring in the discipline of International Relations.Michael Brecher, "International Studies in the Twentieth Century and Beyond: Flawed Dichotomies, Synthesis, Cumulation," International Studies Quarterly 43/2 (1999) 213-264. Back.

Note 84:  Brams, Theory of Moves, 24. TOM is played according to six basic rules:

1. Each game starts at an initial state, which is a previous outcome.
2. Either player can move and change strategies first, becoming Player 1.
3. The other player then can make a countermove.
4. When a state is reached from which neither player prefers to move, the game ends at this "final state".
5. A player will not move from the initial state if it will it ends up in a worse state or returns to the initial state.
6. Both players consider each other's potential future moves in reaching this decision.  

Back.

Note 85:  This is the scenario Zagare argues is closer to true mutual nuclear deterrence, meaning that a nuclear exchange (r₄ ) is preferred to defeat (r₂). Back.

Note 86:  Avner Cohen and Benjamin Frankel, "Opaque Nuclear Proliferation," In Benjamin Frankel, ed., Opaque Nuclear Proliferation: Methodological and Policy Implications (London: Frank Cass, 1991), 32. Back.

Note 87:  Iran also bombed Iraqi cities, but its missile capability was limited and failed to match the devastation inflicted by the Iraqis. Back.

Note 88:  Iranian use of chemical weapons against Iraqi troops is not as well publicized, perhaps due to the fact that the use was limited and ineffectual as Iranian chemical capability was quite primitive compared to Iraq's chemical arsenal and delivery capability Anthony H. Cordesman and Abraham R. Wagner, The Lessons of Modern War, Volume II: The Iran-Iraq War (Boulder: Westview Press, 1990), 517-518; and Office of the Secretary of Defense, Proliferation: Threat and Response (Washington, DC: Department of Defense, April 1996), 15). It is interesting to note, however, they did cross the infamous WMD 'line' which violates international norms and should have produced extreme condemnation. The lesson may not be lost on these two antagonists in future conflicts, since the outside world does not appear to dole out consistent levels of punishment for WMD violations. Back.

Note 89:  This is game #9 from Brams, Theory of Moves. Interestingly enough, preliminary analysis into other dyads, such as a symmetrical Type II-II and the asymmetric Type I-II, indicate games of Prisoners' Dilemma and Called Bluff, respectively, providing support for realist assumptions underpinning Classical Deterrence Theory. This also will be the subject of further research on the NAG. Back.

Note 90:  Backward induction is "a reasoning process in which players, working backward from the last possible move in a game, anticipate each other's rational choices," Brams, Theory of Moves, 220. Back.

Note 91:  Ibid., 224. Back.

Note 92:  Ibid., 94-102, 121-156. Back.

Note 93:  Ibid., 224-225. Equally disturbing, the result in standard game theory, or the Nash equilibrium, also is (3,3) for this game. The Nash concept refers to an outcome from which neither player would have a unilateral incentive to move. Each of the other three outcomes fails this test, e.g., R would want to move from (2,2) to (4,1). So (3,3), meaning mutual nuclear use, is the predicted result. Back.

Note 94:  Further empirical work in this area naturally would depend on databases such as the International Crisis Behavior (ICB) Project. Recent examples indicating ICB's extraordinary range of subjects related to crises include Carment on ethnopolitics, Harvey on deterrence and Rioux on bargaining. David B. Carment, "The International Dimensions of Ethnic Conflict: Concepts, Indicators and Theory," Journal of Peace Research 30 (1993), 137-150; Frank Harvey, The Future's Back; and Jean-Sebastien Rioux, "A Crisis-Based Evaluation of the Democratic Peace Proposition," Canadian Journal of Political Science 31/2 (1998), 263-283. Back.

Note 95:  According to Herring's typology, the US would seem to reflect the 'conservative' perspective of the label 'rogue state'. Eric Herring, "Rogue Rage: Can We Prevent Mass Destruction?", Journal of Strategic Studies 23/1 (2000). Back.