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A Brinkmanship Game Theory Model of Terrorism

Francois Melese and Diana Angelis
Defense Resources Management Institute (DRMI)
School of International Graduate Studies
Naval Postgraduate School
Monterey, CA 93943

Abstract:

What is clear is that any attempted preemptive move against elusive terrorist targets is risky (especially against those with newly acquired WMD capability). A credible threat of preemptive retaliation against terrorists having acquired WMD is likely to weigh heavily on terrorist organizations. Retaliation will have very bad consequences (negative payoffs) on the terrorist organization, but those retaliating are also clearly at risk, as are innocent civilians. In fact, in the event of substantial collateral damage to innocent civilians the blame could ultimately be shifted onto those engaged in retaliation (for example the United States and its "coalition of the willing"). Nobody is likely to escape harm. A Brinkmanship strategy always involves a probabilistic strategic action (preemptive retaliation in this case) that has a mutually harmful outcome. Retaliation might be bad for the terrorists, but it is also bad for those that must carry out the threat. The objective is to make the brinkmanship threat a sufficiently credible and unpleasant option that it deters terrorists from using WMD, while not being so catastrophic and repugnant to those that would have to carry out the threat that they would refuse to retaliate. The paper derives two incentive compatibility or "credibility" constraints that must be satisfied for the UN to adopt a brinkmanship strategy. The first relates to the type of terrorist organization one is up against (Hard or Soft), and the second to risks associated with retaliation. A graphical interpretation of the results reveals when a brinkmanship threat is credible (a set of incentive compatible Nash equilibrium solutions) and when it is not. The final section attempts to address two key categories of risk - "Type risk" (understanding the type of terrorist we face) and "Retaliation risk" (understanding the likelihood of retaliation). Monte Carlo simulations are run that combine distributions over the probability we face a certain "type" of terrorist, with distributions over the probability of "retaliation". The resulting discrete probability distributions reveal conditions under which a brinkmanship strategy is likely to succeed in deterring terrorists from using WMD.