The payoff matrix below shows thevNMutilities (or payoff) of an imaginary game where Player 1 playsUp andDown strategies against Player 2'sLeft andRight strategies.

Player 2

L R

U (-1,-1) (7,0)

player 1 D (0,5) (1,1)

a) Find the pure-strategy Nash equilibrium, if any.(1point)(1point)

b) Derive players' expected payoff functions and best response options to maximize expected payoff when both players adopt mixed strategies.(5+5point)(5+5point)

c) Draw their best response functions on a diagram and clearly indicate the pure and mixed strategy NE.(3point)(3point)

d) Calculate players' expected payoff for the mixed strategy Nash equilibrium.(1point)