Colonel Blotto in the War on Terror: Implications for Event Frequency

Abstract

The U.S. private terrorism-insurance market has failed to develop as hoped under the Terrorism Risk Insurance Act (TRIA) of 2002 and the Terrorism Risk Insurance Extension Act (TRIEA) of 2005. The principal reason that terrorism risk is viewed as uninsurable in conventional insurance markets is the great difficulty in predicting both its severity and frequency components. While the insurance industry has made some progress in forecasting loss severities, there has been little research on terrorism loss frequency. In this article, we extend the work of Major (2002) by employing a formal Colonel Blotto game to investigate the frequency of terrorist attacks. In two different constant-sum scenarios – simultaneous multiple attacks and single random attacks – our equilibrium solutions demonstrate that both sides (terrorists and counter-terrorists) will choose to allocate their forces to all targets in proportion to the square roots of the targets' physical volumes. In the case of single random attacks, the equilibrium frequency results are consistent with Woo's (2005) "principle of target substitution," and provide guidance for the pricing of terrorism insurance.