Economics 201B: Final Solution
Winter 2015
1. Keynes Guessing Game
If player i plays 100,
ui p100, ai q
#
1
N
0
if aj 100, for all j i
otherwise.
If player i plays the following mixed strategy
1
1
1
Lecture Notes for Economics 203
Core Economics III
Game Theory, Imperfect Competition, and Other
Applications
B. Douglas Bernheim
Department of Economics
Stanford University
[email protected]
Lecture 2 - Dominance and Best Responses
Econ 201B Winter, 2018
What is Game Theory?
Game theory is a tool to analyze interaction among a group of rational, strategic agents.
Denition 1 A game in norm
Solutions to Econ 201B Practice Problems 1
Zhuoran Lu
January 16, 2017
1
The Wrong Book
I would represent the game as an infinite-period bargaining game. However, there are many
possible answers for t
Econ 201B
Winter 2018
Homework 1: Dominance, Rationalizability
The due date for this homework is Monday January 22nd in class.
1. Rationalizability: Consider the following game in normal form, where p
Econ 201B
Winter 2018
Homework 2: Equilibria
The due date for this homework is Monday February 5th in class.
1. Nash Equilibrium and Rationalizability: Consider a nite game, and suppose that
it is dom
Econ 201B Spring 2018
Practice Problems 2
You do not need to submit answers to these problems. I still encourage you to
think them through thoroughly, write down your answers and discuss them with
you
Solutions to Econ 201B Homework 1
1
Question 1
(a) For Player 1, E is strictly dominated by C. For Player 2, e is strictly dominated by a. c
is weakly dominated by b and the strictly dominated ones ar
Lecture 4 - Nash Equilibrium
Econ 201B Winter, 2018
Coordination and Anti-Coordination Games
Coordination
Two friends have gone to Disneyland together and lost each other there. There are two focal
po
Solutions to Econ 201B Practice
Problems 2
January 24, 2018
1
Nash Equilibria
Note that equilibrium strategies of NE are (supported by) rationalizable
strategies by the denition of NE and rationalizab
Lecture 3 - Rationalizability and Weak Dominance
Econ 201B Winter 2018
A Beauty Contest
Each student chooses a number between 1 and 100. The student whose number is closest to
2/3 of the average of th
Lecture 9: Extensive Form Games, II
As we have seen, extensive form games with perfect and complete information are easy to model and the assumption of subgame perfection makes
them easy to analyze. B
GAMES OF INCOMPLETE INFORMATION, CONCLUSION
1
Example 4:
Matching pennies with cheating
Actions & Payoffs
H
T
H
(+2,-2)
(-1,+1)
T
(-1,+1)
(+1,-1)
2
COL is unsure if ROW honest or cheater
honest: cann
Economics 201B HW #5
Due Tuesday February 18 in class
In class we showed (for the Cournot game) that thinking about a game in
normal form simultaneous moves and in extensive form sequential moves
can
Midterm solutions
Problem 1.
(a) There is no domination for player 1. For player 2, R is never best response,
so lets check if it is dominated by pL + (1 p)M :
5p + 3(1 p) > 4
2p + 8(1 p) > 6
Thus, 12
Economics 201B HW #3: Solutions
1. Solution
P
(a) The payoff function for each firm is given by i (qi , qi ) = a b Nj=1 q j c qi .
Taking the first order condition with respect to qi , imposing symmet
Economics 201B Midterm Exam
Due: Tuesday February 11, 2014 at beginning of lecture
You may use your own class notes and any material posted on the class
website. You may NOT consult any other material
Lecture 8: Extensive Form Games, I (cont.)
Example 4: Stackelberg Competition
firms 1, 2; produce identical product
market inverse demand function p = 1 (q1 + q2 )
today: firm 1 commits publicly to
Economics 201B Final Exam Solutions
1. Solution
(a) For row player, B is dominated by pA + (1 p)C where p > 12 . Eliminating B, we obtain the matrix
X
A (2,5)
C (3,0)
Y
(4,4)
(2,2)
Z
(2,3)
(4,1)
Then
Economics 201B HW #4: Solutions
1. Solution The minmax payoffs for ROW and COL are (1,1). The strategy
profiles that produce these minmax payoffs are that ROW plays D with probability 1 and COL plays
Lecture 7: Extensive Form Games, Part I
Up to this point we have considered only static games; we now turn to dynamic games. One way to view the distinction is to think of the action as
taking place a
Suggested Solution for Practice Problem 3
by Ziyan Huang 1
1. See Handout for Week 6.
2. Consider the following strategy:
Phase I: Follow the strategy profile (CD,DC,CD,. . . ). If deviate, go to
Phas
Suggested Solution for Practice Problem 1
by Ziyan Huang 1
1. Nash equilibria in pure strategies are cfw_(C, C), (D, D).
Then let us look at Nash equilibria in mixed strategies. Assume that row
player
Professor B. Douglas Bernheim
Economics 203
Winter 2009-2010
Problems
Strategic Environments
1. Consider the following game. There are two players, 1 and 2. They
will play either matching pennies vers
Lecture 5 - Mixed Strategies
Econ 201B Winter 2017
Examples
We have seen many examples of games where Nash equilibria (in pure strategies) exist, e.g.
the Prisoners Dilemma, Cournot competition etc. H