A student, player 1, has to hand in a problem set at the other end of (a large) campus but
needs to rush into an te\st. They have two options. They can deliver the problem set after the te]st (call this option H for "hand-deliver") and incur a late penalty. Alternatively she can give the problem set to
player 2, a random student who happens to be next to player 1 (call this option G for "give"). Player 2
can then either deliver the problem set on time (call this option D for "deliver") or throw it away in the
nearest trash can (call this option T for "throw"). For player 1 the payoff is 1 if the problem set is delivered
on time, −1 if it is thrown away, and 0 if it is delivered late. The payoffs for player 2 are x if they delivers
and y if they throw it away.
(a) Draw the game tree that represents this game. Using some equilibrium consideration, under what
conditions on x and y can we justify player 1 trusting player 2 to deliver the problem set ?
(b) Now assume that a proportion p of the students one might meet on campus are "altruistic" ( A) : they
like to help and have payoffs given by x =1 and y =0. The remaining proportion 1 −p is "mean" (M )
and have payoffs x =0, y =1. You can think of the game now as Nature first drawing the type of
player 2 that player 1 will meet (but player 1 does not observe that type). Draw the new game tree.
(c) Now assume p =3/4. What are the pure-strategy Bayesian Nash equilibria of this game ?
(d) Are there BNE that are not weak perfect bayesian equilibria ? For which values of p are all the BNE
also wPBE ?