Smallpox, risks of terrorist attacks, and the Nash equilibrium: an introduction to game theory and an examination of the smallpox vaccination program.

INTRODUCTION The smallpox vaccination emergency preparedness program has been unsuccessful in enrolling sufficient numbers of healthcare workers. OBJECTIVE The objective of this study was to use game theory to analyze a pre-event vaccination versus post-event vaccination program using the example of a terrorist considering an attack with smallpox or a hoax. METHODS A three-person game (normal and extensive form), and an in-person game are played for pre-event and post-event vaccinations of healthcare workers facing the possibility of a smallpox attack or hoax. RESULTS Full pre-event vaccinations of all targeted healthcare workers are not necessary to deter a terrorist attack. In addition, coordinating vaccinations among healthcare workers, individual healthcare worker risk aversion, and the degree to which terrorists make the last move based on specific information on the status of pre-event vaccination all greatly impact strategy selection for both sides. A Nash Equilibrium of pre- and post-event vaccination strategies among a large number of healthcare professionals will tend to eliminate the advantage (of the terrorists) of a smallpox attack over a hoax, but may not eliminate some probability of a smallpox attack. CONCLUSIONS Emergency preparedness would benefit from game theory analysis of the costs and payoffs of specific terrorism/counter-terrorism strategies.