MS&E 246
Final Examination
Ramesh Johari
March 18, 2009
Instructions
1. Take alternate seating.
2. Answer all questions in the blue books provided. If needed, additional paper will be avail
able at the front of the room. Answers given on any other paper will not be counted.
3. Notes, books, calculators, and other aids are not allowed.
4. The examination begins at 7:00 pm, and ends at 10:00 pm.
5. Show your work! Partial credit will be given for correct reasoning.
Honor Code
In taking this examination, I acknowledge and accept the Stanford University Honor Code.
NAME
(signed)
NAME
(printed)
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Problem 1 (30 points)
. 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.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '07
 JOHARI
 Game Theory, Nash, subgame perfect Nash

Click to edit the document details