The Limits of Classic and Perfect Deterrence Theory: A Game-Theory Analysis of the United States-North Korea Nuclear Standoff

Introduction

At face value, North Korea’s announcement that it will commit to denuclearization is puzzling. Why would a small state–just after having consolidated its deterrent capabilities by successfully testing intercontinental missiles–agree to give up its nuclear arms? In the absence of radical change in international norms, it seems constructivist explanations are not satisfactory (Tannenwald 1999, Howard 2004). Similarly, quantitative and qualitative studies are yet to account for circumstances under which one actor in a dyad of deterrent-parity relinquishes its deterrent force i.e. why a country would give up its source of deterrence (Bell 2017, MccGwire 2006, Quackenbush 2006, Rauchhaus 2009, Morgan 2012, Bell and Miller 2015).

In this essay, I attempt to explain North Korea’s concession by reference to game theory. The two main game-theoretic accounts of nuclear deterrence, Classical Deterrence Theory (CDT) and Perfect Deterrence Theory (PDT), operate under different assumptions. The case of the United States-North Korea standoff (henceforth US-NK standoff) is a test to the explanatory power of both accounts. I find that neither can offer consistent explanations of North Korea’s decision to hold denuclearization talks. First, I show that the hypotheses predicted by CDT are both contradictory and untenable. Second, I test PDT, and find two kinds of problems: failure to predict outcome and methodological limitation.

This essay proceed as follows. Section 2 highlights the most relevant literature on nuclear deterrence and the US-NK standoff, as well as the two literature gaps this essay aims to fill. Section 3 compares the respective theoretical frameworks of CDT and PDT, and lays out the paradox generated by CDT. Section 4 outlines this essay’s methodology. Section 5 explicates this essay’s core findings, which show PDT’s incapacity to explain the outcome of the US-NK standoff. The implications of these findings are discussed in section 6.

Literature Review

Existing scholarship on nuclear deterrence and the US-NK standoff studies these phenomena under different lenses. One substantive field of scholarship concerns itself with the theory of deterrence.[1] Most importantly for this essay, a divide exists between formal theories and quantitative/qualitative analyses. Game-theoretic analyses are the most popular among the formal theory camp. Whilst Morgan (2003) considers the different approaches as distinct theories, Zagare (2004) groups these into two main categories: classical and perfect deterrence theory.[2] The main argument in favor of PDT is that the assumptions on which CDT is predicated lead to a contradiction, known as the “mutual deterrence paradox” (Quackenbush 2010a, 751).[3] The main gap in this literature is empirical applications of deterrence theories. Only Quackenbush (2010b) has empirically tested PDT, and found preliminary support for PDT. The quantitative analysis of PDT’s independent variables found statistically significant correlations to predicted outcomes. Nevertheless, further empirically-based research needs to be conducted to ascertain the robustness of these correlations (ibid.,81).

Quantitative and qualitative analyses, albeit empirically-driven, rarely link back their findings to theoretic accounts. The overarching trend is to question the Mutually-Assured-Destruction Theory, and show the implications of nuclear arms on foreign policy. Bell (2015, 2017) finds that the claim that nuclear arms acquisition emboldens states is reductive, and shows it can have different effects, ranging from increased aggression and expansionist intents, to willingness for compromise. Similarly, Morgan (2012) and Sobelman (2016) support the unpredictability thesis by arguing that nuclear deterrence does not work where stability is poor e.g. against terrorist groups. In their quantitative analysis of both symmetric and asymmetric nuclear dyads, Bell and Miller (2015) further question the effects of nuclear weapons by demonstrating that nuclear proliferation has no significant effect on conflict i.e. it neither increases nor decreases stability. Focusing on historic cases, Ward (2008) argues that nuclear deterrence can equally well be accounted for by other variables, therefore, calling nuclear deterrence a “myth.” That no game-theoretic empirical study has been conducted on the US-NK standoff constitutes the second literature gap this essay aims to bridge.[4] In brief, this essay’s aim is to apply PDT to the NK-US standoff, and draw conclusions in relation to the empirical findings highlighted above.

Theory

Game-theoretic models of deterrence distinguish between two players: the challenger and the defender. These players are always given two choices: to defy (D), or to concede (C). The game unfolds in nodes i.e. occasions for decision-making. For instance, in node 1 the challenger must take a decision (defy or concede), in node 2 the defender must respond with another decision (defy or concede), etc. The game can have a maximum of three nodes. The game finishes when it reaches an equilibrium which can take either of four outcomes: Status Quo, Defender Concedes, Challenger Concedes, or Conflict (Zagare and Kilgour 1993, 4-9).

Classical Deterrence Theory (CDT) hinges on three assumptions: undifferentiated and rational actors; an anarchic international sphere; conflict constitutes the worst outcome for actors (Zagare 2004, 109). CDT explains the effectiveness of nuclear deterrence by highlighting that it raises the cost of conflict to such an extent, that no nuclear state is willing to challenge the other (Quackenbush 2010a, 748). Because of this undesirability of conflict, the security dilemma is eliminated i.e. states no longer see a rival’s defensive military build-up as a security threat (Heywood 2011, 19).

CDT generates three hypotheses. First: because nuclear parity increases safety and states want to increase safety, rational actors would welcome nuclear proliferation. Thus, CDT would predict that the U.S. would welcome NK’s acquisition of nuclear weapons. This hypothesis is non-sensical, since it corresponds to the mirror opposite of what occurred. Second: because nuclear arms make conflict the worst possible outcome, rational actors will prefer to capitulate over start a conflict. Thus, CDT would predict that the U.S. and NK would not come into conflict. Third: because challengers know that defenders will always capitulate, since the defender’s rational impulse is to avoid conflict at all cost, rational challengers should attack. Thus, CDT would also predict that e.g. the U.S. (challenger) would start a conflict with NK (defender) which would, in turn, capitulate. These contradicting hypotheses illustrate the “paradox of mutual deterrence” which shows that for any decision taken, the actors will have acted irrationally (Quackenbush 2010a, 751).[5] In consequence of this paradox and the first hypothesis’ untenability, CDT cannot be tested.

Perfect Deterrence Theory (PDT) holds three different, but somewhat isomorphic, assumptions. First, actors are rational. Second, PDT differentiates between soft and hard players–where conceding is the worst outcome for hard players, and conflict is the worst outcome for soft players. Third, the international sphere is hierarchical as a result of this differentiation. The outcome of a game not determined by the cost of conflict, but by the players’ preferences. Depending on whether the actors are soft/hard players, three possible outcomes are predicted, listed below.

FIGURE 1 Game-Theory Decision Tree

TABLE 1 Four Possible Outcomes in CDT and PDT

TABLE 2 Theoretical Comparison of CDT and PDT

PDT characterizes actors along three independent variables: capability, credibility and player-type. Capability refers to an actor’s military capacity. Credibility is an actor’s perceived willingness to use its deterrent threat i.e. to employ its capacity. Thus, the higher the perceived probability that a player would prefer to execute its deterrent threat, the higher its credibility. The value of these variables dictate the actors’ preferences i.e. its player-type (‘soft’ or ‘hard’ player). PDT generates three sets of hypotheses, each dependent on the characterization of the players (Quackenbush 2010b, 64-65).

1. If the Challenger prefers the Status Quo to Defender Concedes, then the outcome will be Status Quo–regardless of the Defender’s capability.
2. If the Challenger prefers Conflict to Status Quo, and the Defender lacks capability, then the outcome is:
   • Conflict, if Defender is Hard; or
   • Defender Concedes, if Defender is Soft.
3. If the Challenger prefers Conflict to Status Quo, and the Defender has capability and intermediate or low credibility, then the outcome is:
   • Conflict, if both players are Hard;
   • Defender Concedes, if Defender is Soft and Challenger is Hard; or
   • Status Quo, if Challenger is Soft.

Thus, depending on how we characterize the U.S. and NK respectively, we should find that at least one of these predictions holds true. If not, we must reject PDT. In the following section, I will enunciate the method through which both players will be characterized.

Methodology

Having ruled out the alternative explanation of CDT, I will present this essay’s research design. I explicate the case-selection, the method for operationalizing PDT’s dependent variables, the independent variables, and the process for testing PDT’s hypotheses.

Case selection has been one big obstacle to empirical analyses of game-theoretic models.[6] The criterion for this essay’s case-selection consists in identifying dyads which have opportunity for conflict, so-called “politically active dyads” (Quackenbush 2010b, 67). The US-NK standoff fulfill two of the characteristics enumerated by Quackenbush (2006). First, “one of the dyad members is a global power,” namely, the U.S. Second, “one of the dyad members is a regional power in the region of the other,” the U.S. is a regional power in East Asia (Futter and Zala 2015).[7] The NK-US standoff constitutes a disciplined interpretive case study, as this essay’s main goal is to explain a recent event by “applying a known theory [PDT] to [a] new terrain” (Odell 2001, 163).

The three independent variables–capacity, credibility, and player-type–will be operationalized in the following manner. The composite indicator of national capabilities from the Correlates of War project (Singer, Bremer, and Stuckey 1972) will serve as the measure for a state’s military capability.[8] I use the Composite Index of National Capability (CINC) score. This score ranges between 0 and 1, where 0.0 indicates “that a state has 0% of the total capabilities present in the system in that year,” while 1.0 indicates that “the state had 100% of the capabilities in a given year” (ibid. 7). The latest data, from 2012, is taken to be representative of the present state of affairs. The country’s score will be classified into five levels, thus making capability an ordinal variable. Given that there are 195 entries for 2012, the countries are divided into five quintiles of 39 countries each. Countries in the upper quintile will be given a ‘very high’ capability, and in decreasing sequence, countries in the following quintiles will be attributed a ‘high’, ‘medium’, ‘low’ and ‘very low’ capability.

For operationalizing credibility, Quackenbusch (2010b, 71) calculates the probability that an adversary will perceive a threat by means of a mathematical formula which weighs in five factors:

• The size of demand made by state A,
• The probability that A wins,
• The domestic political cost associated with use of force by A,
• The domestic political cost associated with giving in by A,
• The domestic political cost associated with a conflict by A.

Although these are reasonable indicators of credibility, it is problematic to operationalize them with a single numeric value.[9] Therefore, it is better done in an ordinal sequence composed of three values, ‘low’, ‘intermediate’ and ‘high’, where each corresponds to ‘1’, ‘2’, and ‘3’, respectively. Each factor will be considered independently for each state, and the aggregate mean value of the five factors will be rounded to the closest natural number, providing a general score for a state’s credibility. Factor (iv) will not be included due to this essay´s space-constraints and considerable overlap with (iii).

The last independent variable, soft-hard player, is virtually impossible to operationalize in a manner that allows for prediction. In virtue of Quackenbusch’s (2010a) study being quantitative, this issue was circumvented by testing the correlation between outcome and each of the four different possibilities in a dyad (soft-soft, soft-hard, hard-soft, hard-hard). Thus, the dependent variable was chosen a posteriori, depending on the statistical significance. In this study, I will adopt a similar approach i.e. I will infer the player’s preference from the game’s outcome.[10]

The dependent variable is the outcome of the game-theoretic model (c.f. table 1). Although the outcome of the US-NK standoff has already occurred, the event must be interpreted within the parameters of PDT. As such, the outcome will need to be a coherent consequence of the causal path presented in the unfolding of the game-theoretic model. Non-game-theoretical models fall beyond the scope of this essay,[11] wherefore, the only relevant alternative hypothesis, CDT, need not be disproved as it has already been established to be logically incoherent.

Findings

I present my findings in three steps. First, I present the values for capability and credibility. Second, I simulate the nuclear standoff. Finally, I interpret the results.

Dependent Variables

The United States holds 13.94% of the international system’s military capabilities, the second highest CINC score i.e. upper quintile­. Therefore, US capability is ‘very high’. North Korea holds 1.33% of the international system’s military capabilities, 17^th highest in CINC i.e. upper quintile, wherefore, NK’s capability is also ‘very high’.

• The size of demand made by state A.

Under the administration Trump, the United States increased its demands by imposing new UN sanctions, deploying the Terminal High Altitude Area Defense (THAAD) to South Korea, and exacerbating its rhetoric e.g. the Trump’s “fire and fury” remark (Lu 2017). Thus, it merits ‘high’ credibility. North Korea has held its demands constant in the last decade and a half (Futter and Zala 2015). Its demands are explicitly stated in the law passed by the Supreme People’s Assembly: “nuclear weapons of the DPRK are just means for defense . . . [to deter] the US and its nuclear threat” (Korean Central News Agency 2013). Therefore, the value is ‘intermediate.

• The probability that A wins.

US conflict with NK would be too costly (Bleiker 2003, Choi 2015). The US has an interest to protect its allies, South Korea and Japan, which would be in direct jeopardy in case of conflict, thus, decreasing the likelihood of a favorable outcome (Jang 2018). Furthermore, the US lacks operational capability (Wolfstahl and Dalton 2017). Thus, the US value is ‘low’. Conversely, NK would not fare well either. However, its capacity to threaten US core interests is considerable enough to render its value ‘intermediate’ (Howard 2004).

• The domestic political cost associated with use of force by A.

In 2017, whilst 82% of republicans supported a hypothetical war, only 37% of democrats shared the same view (Gallup 2017a). This partisan divide would be a big obstacle for political support, for which reason the US has a ‘low’ credibility-value. Contrastingly, a similar decision in North Korea would not bear any comparable political cost, as it is a one-party state known for having officials with highly compliant and homogenous views (Pak 2018). Therefore, NK’s credibility is ‘high’.

• The domestic political cost associated with a conflict by A.

The support for a war in the US is low. In 1950, 60% of Americans did not support the use of nuclear arms in the nuclear war (Gallup 2017b). This fracture and negative historical precedent contrasts with the support of 58% for the use of military action “if peaceful means [failed]” (Gallup 2017c). The U.S. value is ‘intermediate’. North Korea, in virtue of its authoritarian structure, need not concern itself with public opinion. Furthermore, it has clearly defiend the circumstances under which it would use force. These two combined yield a ‘high’ credibility value.

In account of the scores for each of the five factors, the mean values are 1.8 for U.S. and 2.6 for NK. Rounded to the closest natural number, the US has ‘intermediate’ credibility, and NK has ‘high’ credibility.

TABLE 3 Values of Dependent Variables

The values for player-type will be justified after the game-theoretic modelling. Given these values, PDT would predict that the outcome is (c.f. section 3 for reference of all predictions in relation to player’s characteristics):

• Conflict, if both players are Hard;
• Defender Concedes, if Defender is Soft and Challenger is Hard;
• Status Quo, if Challenger is Soft.

Game-Theoretic Outcome

The standoff is modelled from two perspectives. In progression 1 NK will be the Challenger, and the US will be the Defender. Progression 2 inverses the roles. Progression 1 starts with NK defying (D) the status quo (node 1) by announcing its secret nuclear program after withdrawing from the Nuclear Proliferation Treaty in 2002, followed by its ICBMs tests. Subsequently (node 2), the U.S. defies (D) NK: it enacts sanctions, deploys THAAD to South Korea, and Trump adopts a feisty rhetoric. NK (node 3) then concedes (C) by agreeing to hold talks. Thus, the outcome is Challenger Concedes, which was not predicted by PDT.

FIGURE 2 Progression 1 of US-NK Standoff

Progression 2 begins (node 1) with US-policies in the territorial vicinity of NK defying (D) the status quo. In response (node 2), North Korea defies (D) by pursuing its nuclear ambitions. The model predicts that the US (node 3) would have to accept North Korean proliferation (C), or engage in conflict (D). However, neither of these scenarios took place. Instead, North Korea’s agreement to denuclearize amounts to Defender Concedes. Thus, PDT not only fails to predict, but is incapable of accounting for outcome in progression 2.

FIGURE 3 Progression 2 of US-NK Standoff

Interpretation and Reflection

These findings pose two main problems for PDT. First, the outcome of progression 1, which had not been predicted, casts doubt on PDT’s predictive capacity. This lack of predictive power challenges the relevance of PDT’s dependent variables. For instance, one would expect NK to have won the standoff given that it held a higher credibility-value, and capacity was equal for both players. Second, the methodological limitation of PDT i.e. requiring the researcher to assign a value to one of the dependent variables (player-type) a posteriori, is not a tolerable limitation. Given that a soft-player is defined as one who prefers concession over conflict, and NK exhibited that preference in node 3 of progression 1, NK was characterized as ‘soft’. Conversely, it is impossible to assert the US’ preference because in node 3 of progression 2, where this preference would have been exhibited, NK’s decision to hold talks inhibited the game to reach its third node. Not only does this limitation inhibit one from confidently predicting unknown outcomes, the researcher inevitably begs the question. Finally, progression 2’s failure to reach node 3 is most concerning for PDT. It suggests that the model bears some structural limitation which renders PDT unable to even account for why NK held denuclearization talks. In sum, the disciplined interpretivecase of the US-NK standoff provides evidence that PDT cannot be applied to certain empirical cases.

Conclusion

This paper analyzed the U.S.-North Korea nuclear standoff through the lens of two competing game-theoretic theories: classical deterrence theory and perfect deterrence theory. The former fails for logical incoherence, whilst the latter falls short due to lacking predictive capacity and methodological limitation. These findings suggest that game-theoretic models cannot provide explanatory accounts of empirical cases. Future research could address these limitations through a revision of what structural factors of either PDT or the US-NK standoff contributed to this result, and aim to bring about theoretical improvements. Given that these findings are diametrically opposed to Quackenbusch´s (2010b) empirical support of PDT, one cannot exclude the possibility that this essay committed a crucial fallacy.

One might also add the qualification that the North Korean regime’s commitment to denuclearization might turn out to be little more than a symbolic long-term commitment, analogous to the pledge by signatory of states of the NPT to “the goal of a disarmament by the nuclear-weapon states” (United Nations 2018). If this turned out to be the case, the altered outcome of the standoff would warrant a new empirical test of PDT, potentially salvaging the theoretical coherence of its theory. However, given the highly contingent nature of this qualification, future research would be better-guided in reconsidering PDT’s theoretical mold.

About the Author

Dário Kuteev Moreira is a student at Leiden University, the Netherlands, pursuing a BA in International Studies. Dário wrote this paper for a political science module while studying abroad at the National University of Singapore.

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Endnotes

[1] Deterrence, conventionally defined as a preemptive dissuasion of an adversary’s action, is classified into two different types: immediate and general deterrence (Roach and O’Callaghan 2013, 73). The former refers to a relationship in which “one side is seriously considering an attack while the other is mounting a threat to prevent it” (Morgan 1977, 28). The latter refers to a relationship in which both opponents maintain armed forces to regulate dynamics, albeit neither side is mounting an attack (Quackenbush 2010b, 61).

[2] The crucial differences between the two will be outlined in section 3 of this essay.

[3] Further differences lie in how Morgan (2003) denies procedural rationality to actors, whilst Quackenbush (2010a) assumes an instrumental rationality i.e. actors choose the preferred outcome, despite limitations to rational decision-making in virtue of the influence of emotions, lack of information etc.

[4]Current studies on US-NK are written from a normative angle, often highlighting the strategic conundrums the U.S. faces in case a war broke out. (Glaser and Fetter 2017, Futter and Zala 2015, Powell 2003, MccGwire 2006, Daalder and Lodal 2008, Rauchhaus 2009, Wolfstahl and Dalton 2017, Jang 2018, Pak 2018, Choi 2015).

[5] If a challenger decides not to attack, it will have been rational for avoiding conflict, but irrational for not attacking a defender who would inevitably capitulate. Conversely, if a defender decides not to defend, it will have been rational for avoiding conflict, but irrational for not pursuing its own survival (Zagare 2004, 116).

[6] The first quantitative study used “enduring rivalries” as the “cases for the study of” CDT (Huth and Russet 1993, 63). However, given that rivalry is defined as militarized interstate dispute, dyads that did not engage in conflict, e.g. the US-NK standoff, would fall outside the study’s scope (Diehl and Goertz 2000). In other words, since deterrence is about dissuading an opponent from entering conflict, one should consider cases where conflict did not break out, too.

[7] Quotes from Quackenbusch (2006, 43), check original for remaining criteria. The fulfillment of one criterion is enough for a dyad to be considered “politically active.”

[8] The importance of states’ relative military power (i.e. capacity) is an uncontroversial claim in standard deterrence theory, and its importance has been emphasized in previous empirical studies (Heywood 2011, Huth and Russet 1988).

[9] First, albeit more precise on a surface value, a numeric approach forces the researcher to adopt composite indices to capture all of the aforementioned factors. This has been shown to be a fallaciously reductive and misleading exercise which ends up with less precision (Collier and Adcock 1999, Griffiths 2016). Second, the attempt to reduce five unrelated components to one figure risks rendering the very concept of credibility incoherent, which Gerring (1999) emphasizes to be pivotal for a concept’s scientific legitimacy.

[10] Admittedly, this methodological conundrum is a major challenge to PDT’s predictive influence. This point of criticism will be stressed in sections 5 and 6.

[11] For non-game-theoretical explanations see the following. Signorino and Ritter (1999) argue that similarity in foreign policy accounts for outcome of political clashes. Bremer (1992) argues that geographical proximity is associated with higher proneness to conflict-outcome. Finally, Schultz (2001) finds that democracies increases country’s credibility, therefore, influencing the outcome.