uau} I 1. (8 points} (Tadelis 2.2) Recreation Choices: A player has three possible activities from which to choose: going to a football game, going to a boxing match, or going for a hike. The payoff from each of these alternatives will depend on the weather. The following table gives the agent's payoff in each of the two relevant weather events: Alternative Payoff if rain Payoff if shine Football game 1 2 Boxing match 3 0 Hike o 1 Let p denote the probability of rain. (a) (4) Is there an alternative that a rational player will never take regardless of p? (b) (4} What is the optimal decision as a function of p