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:
Let p denote the probability of rain.
a. Is there an alternative that a rational player will never take regardless of p?
b. What is the optimal decision as a function of p?