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 $5,400 in future lifetime earnings and a C is worth $0. Each player exerts some effort by studying. Studying carries a cost of $1,000 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.

a) Is it an equilibrium for each player to study for 1 day? Show your calculations. b) Is it an equilibrium for each player to study for 2 days? Show your calculations. c) If a game with this structure were conducted as an experiment, would the average effort choice be less than, equal to, or greater than the equilibrium level?