1. [7 points] Consider the following game:

A

Row's Payoff=1 H Col's Payoff= 3

Row's Payoff=3 L Col's Payoff= 2

B C

Row's Payoff=0 Row's Payoff=2 Col's Payoff= 4 Col's Payoff= 0

Row's Payoff=5 Row's Payoff=1 Col's Payoff= 1 Col's Payoff= 3

Column Player

Row Player

(a) Find all the pure strategy Nash equilibria, if there is any.

(b) Find a mixed strategy Nash equilibrium different from any of your answers in (a). Row's mixed strategy is __________ [H] + __________ [L]

Column's mixed strategy is _________ [A] + _________ [B] + _________ [C]

(c) What are the expected payoffs of the equilibrium you found in (b)?

Row's Exp. Payoff = ________________________________________________. Column's Exp. Payoff = ________________________________________________.

1. [1' points] Consider the following game: A B C Column Player Row's Payoff=l Row's Payoff=0 Row's Payoff=2 H Col's Payoff= 3 Col's Payoff= 4 Col's Payoff= 0 Row's Payoff=3 Row's Payoff=5 Row's Payoff=1 L Col's Payoff= 2 (101's Payoff= ] Col's Payoff= 3 Row Player (a) Find all the pure strategy Nash equilibria, if there is any. (b) Find a mixed strategy Nash equilibrium different from any of your answers in (a). Row's mixed strategy is [H] + [L] Column's mixed strategy is [A] + [B] + [C] (c) What are the expected payoffs of the equilibrium you found in (b)? Row's Exp. Payoff = Column's Exp. Payoff =