Counterthreat of Attack to Deter Aggression Jin Yeub Kim Department of Economics, University of Nebraska–Lincoln, 730 N. 14th Street, Lincoln, NE 68588, USA

Economics Letters 167C(2018) pp. 112-113

Abstract A crisis begins when a potential aggressor makes a threat of attack against a target state, creating a stalemate. The potential aggressor’s military technology improves over time, but its true military capability or intention is unknown. I show that the more sensitive the target state is to the danger of potential aggression, the greater the chance that the potential aggressor backs down and the lesser the risk of war. By committing to attacking sooner, the target state can increase security from aggression. My analysis provides a security rationale for counterthreatening to attack to prevent the realization of an aggressor attack. JEL Classification: F51, D74, D82, C73 Keywords: International conflict, Security threats, Stalemate, Military technology, Preventive attack

E-mail address: [email protected]

1. Introduction Some states or non-state actors pose threats that trigger hostile stalemates in the shadow of war. For example, North Korea is continuously taking provocative actions such as missile and nuclear tests, instigating an ongoing nuclear stalemate. The intention and the capability to attack, as well as active preparation, that breaches U.N. Security Council resolutions constitutes a threat to international peace and security. The threat might come in the form of illicit militaristic actions including execution of missile tests, unauthorized nuclear developments, or acquisition and accumulation of threatening capabilities.1 In many security crises inflamed by threats of aggression, the technical feasibility of those threats allegedly increases over time but there is incomplete information about potential aggressors’ capabilities or intentions. For example, it is evident that North Korea continues to advance its technological ability to launch nuclear weapons on long-range ballistic missiles; yet the exact status of North Korea’s nuclear and missile programs appears uncertain and the true intentions of its provocations are not perfectly known.2 While uncertainty about potential aggressors may impede efforts to prevent security crises, non-engagement by other states may embolden the threatening capabilities and actions of potential aggressors, significantly magnifying the risk of greater harm. Can the “counterthreat” to use armed force help reduce the escalating danger posed by potential aggressors’ threats of attack? I tackle this question via using a variation of Fearon’s (1994) war of attrition model. My analysis has implications for current diplomatic debates about forestalling security threats and escalation of crises. 1

See Doyle (2008) for historical and contemporary examples of threats to global security. Albright (2017) suggests that North Korea appears to be significantly improving its nuclear weapons arsenal but notes that there is little reliable public information about the exact amount of nuclear weapons that North Korea has. 2

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2. The Model There are two states, A and B. State A is a potential aggressor who initially makes a threat of attack against target state B. This action of blackmailing is not modeled in the game but represents the outset of a crisis that occurs in continuous time. For every finite t ≥ 0, state A can choose to attack, back down, or continue, while state B can choose to attack or continue.3 The crisis ends when either state attacks or when A backs down. The crisis is said to be in stalemate when both states continue. Payoffs are realized only when the crisis ends. If either state attacks, then both states suffer costs for fighting. For i ∈ {A, B}, let state i’s cost of fighting be denoted ci > 0 if A attacks before B attacks, and di if B attacks before A has attacked or backed down. I assume that dB > cB to guarantee that a stalemate might occur in equilibrium, but I need not require that dA > cA in my analysis.4 During a stalemate, state A improves its military technology, which is assumed to be deployed only when A attacks first.5 Then in addition to the fixed costs of fighting, if A attacks first at time t, then A enjoys benefits of using its improved technology equal to mA (t) and B pays costs for continuing the crisis only to be attacked equal to mB (t). For each state i, mi (t) is a continuous and strictly increasing function of t with mi (0) = 0. Lastly, if A backs down before B has attacked, then both states receive zero payoffs. State A’s backing down can be interpreted as demobilizing any alleged threatening capability. Figure 1 illustrates this crisis game with the payoffs indicated for the 0

three cases where, at time t , A backs down or attacks first or B attacks first.6 3

While both states can choose to back down in Fearon’s (1994) model, state B is devoid of an option to back down in my model. This variation is motivated by Doyle (2008, p. 20) who lays out the two options against the threats of armed attack: to employ armed force or to wait. 4 If it were dB ≤ cB , then B would attack immediately so stalemate does not occur. Further, the assumption of dB > cB can be motivated by thinking of B’s war costs as being dependent on how willing the citizens of B are to support the war. It would be easier to elicit citizens’ support when B is attacked than when it takes the initiative to strike first before the citizens observe signs of imminent aggression from A. 5 This assumption is justified by interpreting state B’s attack as a targeted, surgical military strike that immediately eliminates state A’s (improved) military technology at the start of the fighting. 6 I assume away the possibility of transfers for tractability. Further, discounting is omitted for simplicity as in Fearon (1994).

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Figure 1. A Scheme of the Crisis Game

To keep the analysis tractable, I consider linear specifications mA (t) = µt and mB (t) = πt, where µ ≥ 0 and π ≥ 0 indicate how fast stalemate creates “technological” benefits for A and “waiting” costs for B respectively. All of the parameters except µ are common and public knowledge. The µ captures the rate of A’s military technology advancement, which I call A’s militaristic level or type. State A knows its own type µ, but B believes that µ is drawn from a nonatomic distribution over the interval M ≡ [0, µ ¯], where µ ¯  0, with distribution F that has a continuous and strictly positive density f . I refer to this crisis game as Γ.

3. Results State A’s benefits from attacking accumulate as the stalemate continues, hence backing down ultimately becomes undesirable even for the least-militaristic type of A. Hence in any equilibrium of Γ in which both states choose to continue with positive probability, there is a finite level of continuation after which A is not expected to back down. I call this level of continuation a duration of stalemate, the definition of which is analogous to that of a horizon in Fearon (1994). Given this definition, I present four propositions. The first two propositions replicate the results of Fearon (1994) for my setting, and so proofs are relegated to the online appendix: Proposition 1 characterizes a unique duration of stalemate, and Proposition 2 describes the set of pure strategy equilibria in which a stalemate occurs with positive probability.7 7

The online appendix (available at https://sites.google.com/site/jinyeubkim/files/Kim Military Online.pdf)

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Proposition 1. For any equilibrium of Γ in which a stalemate might occur, the duration of stalemate is t∗ = (dB − cB )/π. Proposition 2. The equilibrium strategies for states A and B, as well as B’s beliefs in equilibrium, are given as follows: (i) State As of type µ ≥

cA t∗

attack at time t∗ , whereas As of type µ <

cA t∗

back down at

time t < t∗ where t is chosen according to any pure strategy as a function of µ that
yields a cumulative distribution Q(t)/F ctA∗ on the interval [0, t∗ ], where Q(t) can be
any nonatomic strictly increasing distribution on [0, t∗ ) such that Q(t∗ ) = F ctA∗ .

(ii) State B attacks at time t∗ . For all t ≤ t∗ , B’s beliefs F ctA∗ ; t are F ctA∗ updated using Bayes’ theorem and A’s strategy for backing down. In particular, B believes that


the probability A will back down is F ctA∗ − Q(t) / 1 − Q(t) . For all t > t∗ off the equilibrium path, let B believe that µ > at

cA t∗

and is distributed according to F truncated

cA . t∗

Propositions 1 and 2 imply that there is a set of equilibria involving a stalemate, wherein all have t∗ as the duration of stalemate and neither side initiates war prior to t∗ . These equilibrium features also arise in Fearon’s (1994) setting but with different driving forces. In my setting, B never chooses to attack before t∗ , thus avoiding the risk of an unnecessary war while maximizing the chance of A backing down. State A of a high militaristic level continues up to t∗ so as to accumulate as much as possible of technological benefits from attacking; state A of a low militaristic level would find backing down prior to t∗ worthwhile. There are two aspects of the equilibrium behavior in my crisis game that substantively depart from Fearon (1994). First, while all equilibria have identical behavior up to the horizon time in Fearon (1994), the equilibrium distributions on outcomes up to t∗ differ across equilibria in my game. Second, unlike Fearon (1994) where the states may choose any time to attack after the horizon time, both A (with a sufficiently large µ) and B commit themselves to attack at time t∗ . As the stalemate continues, B’s beliefs that A prefers attacking to provides technical details on the solution concept and the proofs of Propositions 1 and 2.

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backing down increase. By the time the stalemate reaches t∗ , B’s attack becomes rational; the only sorts of A remaining have relatively high militaristic levels, who also find attacking worthwhile. State B’s commitment to attack at t∗ may lock the states into a war while at the same time putting pressure on A with a relatively low µ to back down prior to t∗ . Now I turn to a comparative statics of the equilibrium with respect to π. The parameter π represents B’s sensitivity to escalation of the crisis that leads to the actual realization of A’s threat to attack. Alternatively, π can be interpreted as B’s aversion to stalemate followed by A’s attack. Proposition 3. In any equilibrium of Γ in which stalemate might occur, the duration of stalemate decreases with an increase in π. Further, the risk of an aggressor attack given a crisis decreases with an increase in π. Proof. It is straightforward to see that t∗ = (dB − cB )/π falls with an increase in π. The ex ante probability that A will choose to attack at t∗ , which represents the risk of an aggressor
attack conditional on a crisis occurring (i.e., lasting longer than t = 0), is 1 − F ctA∗ . Then, i  h   

 d 1 − F ctA∗ /dπ = ∂ 1 − F ctA∗ /∂t∗ · dt∗ /dπ < 0. Proposition 3 demonstrates that the more sensitive B is to stalemate that is followed by A’s attack, the shorter the duration of stalemate and the lesser risk of an aggressor attack. While the former effect is in the same spirit as in Fearon (1994), the latter effect is unique to my setting. If B is more susceptible to the threat of attack and the danger of potential aggression, B commits to attacking sooner in equilibrium. Given a shorter period of time to advance its military technology, A accumulates (by continuing the crisis) a lower level of benefits associated with execution of its threat to attack. Thus A is less likely to attack. On the other hand, if B is less sensitive to A’s potential aggression, then the stalemate is expected to last longer at a greater risk of aggressor attack. Finally, Proposition 4 establishes a necessary and sufficient condition under which war occurs with zero probability in equilibrium. 5

Proposition 4. The probability of war for a given crisis is zero if and only if

π dB −cB

≥

µ ¯ . cA

Proof. War can occur only at t = t∗ in equilibrium, so the probability of war given a crisis
cA ≥µ ¯. is 1 − F ctA∗ , which equals zero if and only if ctA∗ = (dB −c B )/π For a crisis to have zero probability of war, the rate at which B’s waiting costs increase must be relatively higher than the maximum possible rate at which A improves its military technology. Roughly speaking, if B fears periods of escalating tensions by far more than A enjoys its rising military capabilities, then war never occurs given a crisis.

4. Discussion: Threat and Counterthreat The results offer implications for the use of armed force as a counterthreat measure, the purpose of which is to forestall the actual execution of potential aggressors’ threats to attack. The leaders in threatened countries can put pressure on a potential aggressor to back out of its threat by committing themselves to attack the potential aggressor after a certain period of time. This strategy can be described as making a “counterthreat” of attack against the potential aggressor’s threat of attack. Paradoxically, the stronger the threatened country’s aversion to aggression, the sooner the threatened country shall commit to turn itself to aggression. But employing such an aggressive military strategy can provide more security from aggressor attacks: If the threatened country can credibly convey its intolerability to a prolonged stalemate in the shadow of unwanted war, then committing to execute its counterthreat of attack sooner will give rise to a greater chance of the potential aggressor’s concessions and a less risk of war. My analysis thus suggests a security rationale for taking an aggressive military stance to counter security threats. I conclude by connecting this paper to two strands of literature. First, it contributes to and expands the line of literature on the prevention of security crises. The literature addresses a wide range of topics, including the deterrence threat of nuclear brinkmanship (Nalebuff, 1986; Powell, 1990), brinkmanship with no commitment power (Schwarz and Sonin, 2008), 6

terrorist and counterterrorist strategies (Kydd and Walter, 2006), counterterrorism policies (Bueno de Mesquita, 2007; Powell, 2007), preventive wars (Doyle, 2008), the relationship between privacy and security from terrorism (Dragu, 2011), and the role of legal limits on executive power in terrorism prevention (Dragu and Polborn, 2014). Second, my paper is related to a large body of the literature on crisis bargaining under incomplete information (e.g. Banks, 1990; Blainey, 1988; Fearon, 1994, 1995; Fey and Ramsay, 2011; Morrow, 1989; Powell, 1987, 1996, 2004; Schultz, 1998, 1999; Slantchev, 2003). I use a variation of Fearon’s (1994) model in which both states can back down and the state that backs down suffers audience costs. My model differs in terms of the states’ possible actions and the payoff structure. These variations stem from different situations of interest. While Fearon (1994) considers crises in the presence of domestic political audiences, which impose greater costs to states as the crisis continues, my paper points to crises in the face of increasing threatening capabilities of states with extreme agendas.

Acknowledgements I am deeply grateful to Roger Myerson, Lars Stole, and Ethan Bueno de Mesquita for their valuable advice and guidance on this paper. I greatly appreciate the feedback from Scott Ashworth, Sandeep Baliga, Thomas Dolan, Tiberiu Dragu, Alex Frankel, Mehdi Shadmehr, Richard van Weelden, and a number of conference audiences. I also acknowledge Jin Young Kim, Charles Lipson, and John Mearsheimer for their insights on international politics. An earlier version was circulated under the title “A Strategy of Counter-Threatening against Security Threats.”

References Albright, David. 2017. “North Korea’s Nuclear Capabilities: A Fresh Look.” The Institute for Science and International Security. http://isis-online.org/isis-reports/category/koreanpeninsula.

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Banks, Jeffrey S. 1990. “Equilibrium Behavior in Crisis Bargaining Games.” American Journal of Political Science 34(3): 599–614. Blainey, Geoffrey. 1988. The Causes of War. Third ed. New York: The Free Press. Bueno de Mesquita, Ethan. 2007. “Politics and the Suboptimal Provision of Counterterror.” International Organization 61(1):9–36. Doyle, Michael W. 2008. Striking First: Preemption and Prevention in International Conflict. Princeton, NJ: Princeton University Press. Dragu, Tiberiu. 2011. “Is There a Trade-off Between Security and Liberty? Executive Bias, Privacy Protections, and Terrorism Prevention.” American Political Science Review 105(1):64–78. Dragu, Tiberiu and Mattias Polborn. 2014. “The Rule of Law in the Fight against Terrorism.” American Journal of Political Science 58(2):511–524. Fearon, James D. 1994. “Domestic Political Audiences and the Escalation of International Disputes.” American Political Science Review 88(3): 577–92. Fearon, James D. 1995. “Rationalist Explanations for War.” International Oranization 49(3): 379–414. Fey, Mark and Kristopher W. Ramsay. 2011. “Uncertainty and Incentives in Crisis Bargaining: Game-Free Analysis of International Conflict.” American Journal of Political Science 55(1): 149–69. Kydd, Andrew and Barbara Walter. 2006. “The Strategies of Terrorism.” International Security 31(1):49–80. Morrow, James. 1989. “Capabilities, Uncertainty, and Resolve: A Limited Information Model of Crisis Bargaining.” American Journal of Political Science 33(4): 941–72. Nalebuff, Barry. 1986. “Brinkmanship and Nuclear Deterrence: The Neutrality of Escalation.” Conflict Management and Peace Science 9(2): 19–30. Powell, Robert L. 1987. “Crisis Bargaining, Escalation, and MAD.” American Political Science Review 81(3): 717–35. Powell, Robert L. 1990. Nuclear Deterrence Theory: The Search of Credibility. Cambridge: Cambridge University Press. Powell, Robert L. 1996. “Bargaining in the Shadow of Power.” Games and Economic Behavior 15(2): 255–89. Powell, Robert L. 2004. “Bargaining and Learning while Fighting.” American Journal of Political Science 48(2): 344–61.

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Powell, Robert L. 2007. “Defending Against Terrorist Attacks with Limited Resources.” American Political Science Review 101(3):527–541. Schultz, Kenneth. 1998. “Domestic Opposition and Signaling in International Crisis.” American Political Science Review 94(4): 829–44. Schultz, Kenneth. 1999. “Do Democratic Institutions Constrain or Inform? Contrasting Two Institutional Perspectives on Democracy and War.” International Organization 53(2): 233– 66. Schwarz, Michael and Konstantin Sonin. 2008. “A Theory of Brinkmanship, Conflict, and Commitments.” Journal of Law, Economics, & Organization 24(1):163–183. Slantchev, Branislav L. 2003. “The Principle of Convergence in Wartime Negotiations.” The American Political Science Review 97(4): 621–32.

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