4. Two chefs are competing for a position at a restaurant called "Food for Thought". The value of the position to each chef is equal to v. The competition takes a form of a contest in which one of the two chefs who bakes a bigger cake wins. In order to bake a cake of size x>0, chef i has to procure x kilograms of flour from the restaurant at a price pi per kilogram. The restaurant will charge a chef for the flour only if he wins the contest. The price of flour pi for each chef i is drawn randomly from a uniform distribution on [1,2]. The prices for the two chefs are independent. The chefs choose the sizes of their cakes simultaneously to maximize the expected value of the position net of the expenses for the flour. (a) Suppose the realized prices for the flour are publicly observed before the chefs make their choices. Let p10, chef i has to procure x kilograms of flour from the restaurant at a price pi per kilogram. The restaurant will charge a chef for the flour only if he wins the contest. The price of flour pi for each chef i is drawn randomly from a uniform distribution on [1,2]. The prices for the two chefs are independent. The chefs choose the sizes of their cakes simultaneously to maximize the expected value of the position net of the expenses for the flour. (a) Suppose the realized prices for the flour are publicly observed before the chefs make their choices. Let p1