. Answer the following questions.
(a) (10 points) Consider a two player simultaneous move game where player 1 has action set
, and player 2 has actions
. 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:
(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
. Find a sufficiently large value of
such that there exists a subgame perfect Nash
equilibrium where, on the equilibrium path, both players play
in every period.