2. Consider a gunfight between Bat Masterson and William "Curly Bill" Brocius. Both of the men have private information regarding their skill with a six-shooter. Nature moves first by determining each gunfighter's skill. He can have either a fast draw or a slow draw. There is a 65% chance that Bat is fast and a 60% chance that Curly ill is fast. After each gunfighter learns his type-though remaining uncertain about the other gunfighter's type - he chooses between draw and wait. If both wait, then the payoff is 50 . If both draw and (1) they are of the same type (either both fast or both slow), then each has a payoff of 20 ; and (2) they are of different types, then the fast gunfighter has a payoff of 30 and the slow one of 40. If one draws and the other waits and (1) they are of the same type, then the one who drew has a payoff of 30 and the other a payoff of 40; (2) the one who draws is fast and the other is slow, then the one who drew has a payoff of 30 and the other a payoff of 40; and (3) the one who draws is slow and the other is fast, then each has a payoff of 20 . If at least one chooses draw, then there is a gunfight. a. Is it consistent with BNE for there to be a gunfight for sure? (That is, both gunfighters draw, regardless of their type.) b. Is it consistent with BNE for there to be no gunfight for sure? (That is, both gunfighters wait, regardless of their type.) c. Is it consistent with BNE for a gunfighter to draw only if he is slow? 2. Consider a gunfight between Bat Masterson and William "Curly Bill" Brocius. Both of the men have private information regarding their skill with a six-shooter. Nature moves first by determining each gunfighter's skill. He can have either a fast draw or a slow draw. There is a 65% chance that Bat is fast and a 60% chance that Curly ill is fast. After each gunfighter learns his type-though remaining uncertain about the other gunfighter's type - he chooses between draw and wait. If both wait, then the payoff is 50 . If both draw and (1) they are of the same type (either both fast or both slow), then each has a payoff of 20 ; and (2) they are of different types, then the fast gunfighter has a payoff of 30 and the slow one of 40. If one draws and the other waits and (1) they are of the same type, then the one who drew has a payoff of 30 and the other a payoff of 40; (2) the one who draws is fast and the other is slow, then the one who drew has a payoff of 30 and the other a payoff of 40; and (3) the one who draws is slow and the other is fast, then each has a payoff of 20 . If at least one chooses draw, then there is a gunfight. a. Is it consistent with BNE for there to be a gunfight for sure? (That is, both gunfighters draw, regardless of their type.) b. Is it consistent with BNE for there to be no gunfight for sure? (That is, both gunfighters wait, regardless of their type.) c. Is it consistent with BNE for a gunfighter to draw only if he is slow