1. Consider the following two-player game. The row player chooses up (U) or down (D). The column player chooses left (L) or right (R). The first number in each cell gives the payoff to the row player, and the second number gives the payoff to the column player. The game is:

   

   1. (a) Suppose the row player chooses U with probability p and chooses D with probability 1 − p. The column player chooses L with probability q and chooses R with probability 1 − q. Find the players’ best response functions, and illus- trate them in a graph.

   2. (b) Find all the Nash equilibria (pure and mixed) of the game. What are the expected payoffs of the players at the mixed strategy Nash equilibrium?
       

U D L 4,2 1,1 R 1,1 2,4