Three men claim to be the fastest gun in the West. To see who is right, they agree to meet at a cemetery, somewhere in a desert. In the center of the cemetery there is a circular, cobblestoned area that is roughly 50 yards in diameter (with the graves surrounding this area—but this is not vital information). Each man stands at the perimeter of the circular area such that each man is equidistant from the other. Each man has one bullet in his gun and one important piece of information in his head: The probability of each man hitting anything he shoots. Good hits his target 95% 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. Note: Running away is not a possible strategy. (5) If this is a simultaneously played game, what is each man’s optimal strategy? Again, you must list their available strategies