Combining game theory and risk analysis in counterterrorism: A smallpox example
The U.S. government wishes to invest its resources as wisely as possible in defense. Each wasted dollar diverts money that could be used to harden crucial vulnerabilities, prevents investment in future economic growth, and increases taxpayer burden. This is a classic conflict situation; a good strategy for the player with fewer resources is to leverage disproportionate resource investment by its wealthy opponent. That strategy rarely wins, but it makes the conflict sufficiently debilitating that the wealthy opponent may be forced to consider significant compromises. Game theory is a traditional method for choosing resource investments in conflict situations. The standard approach requires strong assumptions about the availability of mutual information and the rationality of both opponents. Empirical research by many people [KT72] shows that these assumptions fail in practice, leading to the development of modified theories with weaker assumptions or the use of prior probabilities in the spirit of Bayesian decision theory. This paper considers both traditional game theory (minimax solution for a two-person, zero-sum game in normal form) and also a minimum expected loss criterion appropriate for extensive-form games with prior probabilities. However, we emphasize that for terrorism, the zero-sum model is at best an approximation; the valuation of the wins and the losses is likely to differ between the opponents. Game theory requires numerical measures of payoffs (or losses) that correspond to particular sets of decisions. In practice, those payoffs are rarely known. Statistical risk analysis allows experts to determine reasonable probability distributions for the random payoffs. This paper shows how risk analysis can support game theory solutions and how Monte Carlo methods provide insight into the optimal game theory solutions in the presence of uncertainty about payoffs. 10 David L. Banks and Steven Anderson Our methodology is demonstrated in the context of risk management for a potential terrorist attack using the smallpox virus. The analysis we present here is a simplified version that aims at methodological explanation rather than analysis or justification of specific healthcare policies. As a tabletop exercise, the primary aim is only to provide a blueprint for a more rigorous statistical risk analysis. The underlying assumptions, modeling methods used here, and any results or discussion of the modeling are based on preliminary and unvalidated data and do not represent the opinion of the Food and Drug Administration (FDA), the Department of Health and Human Services, or any branch of the U.S. government. © 2006 Springer Science+Business Media, LLC.
