Question 1. Game Theory

Consider a “divide four objects game” in which player 1 proposes a division scheme ((4,0),

(3,1), (2,2), (1,3) or (0,4)) and player 2 either accepts it or rejects. In the former case, the

proposed division takes place and in the latter both players get nothing.

a) Find the number of different pure strategy Nash equilibria of this game.

b) Find the number of SPE among these Nash equilibria.