Three spies, Smart, Bond, and Reese,4 decide to solve their dierences with a polite

pistol duel. Smart is the worst shooter, having only 33% accuracy. Bond is better,

having 66% accuracy. Reese is the best, having 100% accuracy. The sequence of shots

is as follows: Smart goes rst, followed by Bond, and then Reese, until only one spy

remains.

Each spy has exactly three actions: shoot opponent 1, shoot opponent 2, or purposely

miss. If Smart wishes to maximize his chances of survival, what should he do? Justify

your reasoning.