. Answer the following questions.
(a) (10 points) Consider a two player simultaneous move game where player 1 has action set
{
L,M,R
}
, and player 2 has actions
{
l,m,r
}
. Assume both players receive a payoff of 1 if
they play the same action, and zero otherwise. Give two different extensive form represen-
tations of this game.
(b) (10 points)
True or false
: A weakly dominated strategy is never rationalizable. If true, justify
your answer; if false, give a counterexample.
(c) (10 points) Give an example of a two player game with at least two mixed Nash equilibria
(that are not pure Nash equilibria).
Problem 2 (30 points)
. Consider the following two player game:
Player 2
H
M
L
H
(0,0)
(3,4)
(6,0)
Player 1
M
(4,3)
(0,0)
(0,0)
L
(0,6)
(0,0)
(5,5)
(a) (5 points) Are any strategies strictly dominated?
(b) (5 points) Find all pure Nash equilibria of this game.
(c) (10 points) Find a symmetric mixed Nash equilibrium of this game, i.e., where both players
play the same mixed strategy.
(d) (10 points) Now consider an infinitely repeated game, where both players have discount
factor
δ
. Find a sufficiently large value of
δ
such that there exists a subgame perfect Nash
equilibrium where, on the equilibrium path, both players play
(
L,L
)
in every period.
2