Perfect Nash equilibrium
Two students prepare their homework assignment together for a course. They both enjoy getting high grade for their assignment, but they dislike working on the assignment. They can both choose to supply Low, Medium or High level of effort. Their payoff is given in the table below:
(a) Find all pure-strategy Nash equilibria of this game. Can the efficient outcome be achieved in equilibrium in a one-shot game?
(b) In this course students have to hand in two assignments. Thus, the above game is played twice. Start by assuming that students are very patient (no discounting between the periods). Is there a sub-game perfect Nash equilibrium that can achieve the outcome M-M in the first stage? If yes, describe this equilibrium, otherwise explain why it is not possible. Hint: discuss whether we have a problem with credible threats here.
(c) How does your answer in part (b) change if we now assume very impatient students with δ= 0:3? Provide both calculations and intuition.