Rational deterrence by proxy: designing cooperative security agreements

Abstract

President Obama’s call for change in the conduct of US foreign policy shifts emphasis from direct interventions to cooperative partnerships. With a billion pledge as support for their development, the issue of effectiveness and design is brought to the fore. If terror organizations cannot be eradicated, can a donor state successfully delegate the deterrence or at least the containment of a violent non-state actor to the host country from which it operates? We identify, assess for impact, and value rational delegated deterrence arrangements, in which the US subsidizes a host, and the host, with agreed upon vigor, inhibits the activity of the violent non-state actor operating within its borders. We account for the US’ imperfect monitoring of host and non-state actor activity and identify agreements that can successfully deter the targeted organizations. We also find that mutually agreeable weak cooperation between donor and host can endure despite the survival of the violent non-state actor on host territory.

Keywords:

• Terrorism
• Deterrence
• Game theory
• Design of international agreements

Notes

No potential conflict of interest was reported by the authors.

McDonough School of Business, Georgetown University.

1 Powell (2007), Bier, Oliveros, and Samuelson (2007), and Zhuang and Bier (2007) work out the optimal allocation of security across potential terrorist targets while accounting for the terrorist’s response to this allocation. Caulkins, Feichtinger, and Tragler (2008) are concerned with the optimal use of aggressive countererror measures given their positive impact on terrorist recruitment.

2 Offensive counterterror aims at disabling terror groups and benefits all. By contrast, defensive counterterror hurts alternative targets by making them more vulnerable. These basic incentives lead to an under-provision of offensive counterterror and an over-provision of defensive measures. See among other works, Arce and Sandler (2005), and Bandyopadhyay and Sandler (2011).

3 Bueno de Mesquita (2005) shows how violence might increase as a result of a Government compromise because only the more moderate faction respect the terms of the agreement. Sandler and Siquiera (2006) show that voters’ strategic choice of elected officials exacerbates the under provision of proactive countererror, but voter strategy can also alleviate the over provision of defensive countererror (Siquiera and Sandler 2008).

4 Mantell (2007) constructs of a simultaneous play matrix game between a host and a victim nation to illustrate that allying with the terror group operating on their territory is a dominant strategy for the host if it is available. His analysis underscores the importance of ‘subverting the coalitions between the terrorists and their hosts,’ Mantell (2007), 97.

5 Knopf discusses the various actions that can be taken to deter terrorist activity in his discussion of the fourth wave of deterrence research.

6 Parameters , and are chosen so that the parameter on each player’s control variable is normalized to 1 or . In HO’s payoffs, the terms and should be considered together so that describes how HO benefits from x in a way that depends on how it allocates the aid x (between and ).

7 A more general payoff functional form would involve instead of in order to reflect the net benefits of direct intervention. But, up to subtracting of and dividing all remaining terms by , this is strategically equivalent to the given payoff.

8 For completeness, one may further assume that before the parties agree to such a scheme, the Nash equilibrium of the stage game is in play so that TR’s move before the agreement begins is . As a result, the host is expected to counter with an initial under the agreement’s terms.

9 This statement only holds for the class of agreements we discuss. There may be other agreement designs that are more efficient. One may, for instance, add the choice of a constant that x is held to in compliance. Further analysis shows that a lower benefits US but harms HO’s expected payoffs, thus also resulting in efficiency.

10 The issue of imperfect monitoring was introduced by Green and Porter (1984) in the context of cartel price wars. Monitoring in Green and Porter is imperfect because of uncertainty on the motivation behind cartel member price changes – these could be responses to demand shifts rather than intentional breaches of the cartel’s agreement. In our case, we must account for strategic deviations from the agreement. In this sense, imperfect monitoring is endogenous.

11 We assume that the level of monitoring is exogenous but compare agreement designs across varying levels of monitoring.

12 For simplicity, we assume that the accuracy of observations of TR is common to US and HO, and that the accuracy of the response of HO is common to US and TR.

13 The MPE concept was originally developed with respect to ‘payoff relevant’ histories only. See Fudenberg and Tirole (1991) or Maskin and Tirole (1994). But the MPE has become a standard solution concept in stochastic games independently of this restriction. For a discussion on MPEs in stochastic games see Doraszelski and Escobar (2010).

14 Specifying an initial state is unnecessary since play according to an MPE will always be optimal in any state.

15 It should be noted that any is considered compliant but that US has no incentive to exceed this value. Similarly, HO could choose and TR could choose when undeterred, but none would benefit from it.

16 Of course p and r are related and we will identify the relationship when developing a potential agreement’s value.

17 In this case, it turns out that so that the expected value of is

18 Langlois and Langlois (2001, 2004) develop a measure of international treaty value when cooperation is phased in. Press and Dyson (2012) evaluate the expected payoffs of various strategy profiles through the long-term steady state payoffs of the Markov chain such profiles determine.

19 Langlois and Langlois (2001) show that that the same result for would be obtained if we were to evaluate it using discounted payoff streams in each of the states instead of one-shot payoffs.

20 Given parameter values the maximum acceptable strength for HO is and it requires that the US maintain subsidies at . Agreement values in this case are 2.89 for HO and 4.16 for the US.

22 In any discounted repeated game, if a single deviation is not profitable for a player, any sequence of future deviations will not be profitable either. This principle applies equally to the discounted stochastic games of the next section.

23 When , is merely a polynomial interpolation of degree k in that agrees with the points and is normalized to be a true density.

24 When deterrence fails while . But when deterrence succeeds we will have to consider two cases and depending on what prior state was reached. As a result, will take two possible values and so will the optimal response by HO.

25 This is used numerically in our simulations. When deterrence succeeds, there are two cases: if , and otherwise. This yields two values of in (B17(B17) ).

26 There is no such requirement concerning TR.

27 This last argument shows the tradeoff of a lower r for a higher p. A higher p decreases , thus requiring a longer punishment period to keep HO cooperating.