Suppose that there are three students in a class competing for a grade of A. The way the class is curved, there is only one A is awarded in the class, and the other two students receive a C. An A is worth $5,000 in future lifetime earnings and a C is worth $0. Each player exerts some effort by studying. Studying carries a cost of $500 per day. Each player's probability of winning the prize is proportional to the effort exerted. For example, if student 1 studies twice as much as student 2, student 1 has twice the chance of getting an A as student 2.

b) Is it an equilibrium for each player to study for 2 days?

c) Is it an equilibrium for one player to study for one day and the other two to study for two days?

d) If this game were played as an experiment, would people study for less, more or equal to the equilibrium level?