GraduateGameTheoryHomework3-2012 - Homework Assignment#3...

Homework Assignment #3
Graduate Game Theory
Due Wednesday, February 17th, 2012 at 11:59pm.
Prepare your answers in LaTeX and email to Gordon and Professor Patty.
1. Find all Nash equilibria of this game.
L R
U (3,5) (0,2)
D (0,2) (2,3)
2. Find all Nash equilibria of this game.
3. Consider the following 2 player game. Player 1 names a number, x
1
1
∈ { 1 , 2 } . After this,
player 2 names a number, x
1
2
∈ { 1 , 2 } . Play repeats, with alternating choices, until one
player wins. The winner receives a payoff of 1 and the loser receives a payoff of 0. Answer
the following questions.
(a) Suppose that the winner is the first player after whose choice the sum of all choices
adds up to at least 4.
i. Draw this as an extensive form game.
ii. What is the subgame perfect equilibrium of this game?
(b) Suppose that the winner is the first player after whose choice the sum of all choices
adds up to at least 5. What is the subgame perfect equilibrium of this game?
(c) Suppose that the winner is the first player after whose choice the sum of all choices
adds up to at least 6. What is the subgame perfect equilibrium of this game?