Three men claim to be the fastest gun in the West. To see who is right, they agree to meet at a desolate location in a desert. On a circular, cobblestoned area that is roughly 50 yards in diameter, each stands at the perimeter such that each man is equidistant from the other. Each man has two bullets in his gun and one piece of information. That information is the probability of each man hitting anything he shoots. Good hits his target 100% of the time. Bad hits his target 95% of the time. Ugly hits his target 1% of the time.
Suppose this is a sequential game and Ugly goes first, what is his optimal strategy? To answer this, you must first determine the set of strategies for each man.
If this is a simultaneously played game, what is each man’s optimal strategy? Again, you must list their available strategies.