In studying for his economics final, Sam is concerned about only two things: his grade and the amount of time he spends studying. A good grade will give him a benefit of 20; an average grade, a benefit of 5; and a poor grade, a benefit of 0. By studying a lot, Sam will incur a cost of 10; by studying a little, a cost of 6. Moreover, if Sam studies a lot and all other students study a little, he will get a good grade and they will get poor ones. But if they study a lot and he studies a little, they will get good grades and he will get a poor one. Finally, if he and all other students study the same amount of time, everyone will get average grades. Other students share Sam's preferences regarding grades and study time.
a. Model this situation as a two-person prisoner's dilemma in which the strategies are to study a little and to study a lot, and the players are Sam and all other students. Include the payoffs in the matrix.
b. What is the equilibrium outcome in this game? From the students' perspective, is it the best outcome?