ECON 1870, Spring 2012
Game Theory and Applications to Economics
Brief Solutions to Midterm Exam
Professor: Georoy de Clippel
TA: Suzuki, Takeshi
March 21, 2012
Part 1: Denitions/Theory
a) (5 points)
False.
Consider the following game:
Player 2
R
B
R
1, 1
ECON 1870 - Game Theory and Applications to Economics
Preparing for the Midterm
Georoy de Clippel
Brown University
Format The format of the nal exam will be similar to that of the midterm. It will start
by asking you to dene some important concepts (see l
ECON 1870 - Game Theory and Applications to Economics
Georoy de Clippel
Brown University (Spring 2012)
Final Exam
Duration: 150 minutes. Total score: 95 points.
Permitted materials: non-programmable calculators, English and foreign language dictionaries.
ECON 1870, Spring 2013
Game Theory and Applications to Economics
Solutions to Problem Set 7
Problem 1: (4.1) (10 points)
4,1 0,0
Normal-form game:
3,0 0,1
2,2 2,2
Nash Equlibira: (L, L ), (R, R )
Subgame perfect Nash Equlibria: Since the only subgame is t
Econ 1870, Spring 2015
Problem Set 1: Simultaneous Move Games
Due Wednesday, Feb. 4th, in class or by 5pm to the box in the basement of Robinson Hall.
1
Dominance (20 points)
Consider the simultaneous-move game represented by the following matrix:
T
Playe
Econ 1870, Spring 2015
1
Answers to Problem Set 1: Simultaneous Move Games
Dominance (20 points)
Yes. B is dominated for player 1; after removing B, L is dominated for player 2; after removing L,
T is dominated for player 1; after removing T, R is dominat
Econ 1870, Spring 2015
Problem Set 3: Games with Incomplete Information
Due Wednesday, March 4th, in class or by 5pm to the box in the basement of Robinson Hall.
1
Grab the cake
There is one piece of cake left, and Ed and Louie would both like some cake.
Economics 1870: Game Theory and Applications to Economics
Spring 2015
Instructor:
Name:
Office:
Office hours:
Email:
Class day/time:
Class location:
Course website:
Jim Campbell
Office 106 at 70 Waterman St
Mondays 10:30am-12:00 noon
jimcampbell@brown.edu
Econ 1870, Spring 2015
Problem Set 2: Level k and Sequential Games
Due Wednesday, Feb. 18th, in class or by 5pm to the box in the basement of Robinson Hall.
1
Applying level k (20 points)
Consider the simultaneous-move game represented by the following ma
Information
Econ 1870: Game Theory and Applications to
Economics
Signaling
In the last section we built the apparatus of game theory, and in
particular solution concepts for games with imperfect information.
We saw that settings with incomplete informatio
Strategic Interaction
Goal: analyze situations in which consequences of our choices depend
also on other agents choices.
Econ 1870: Game Theory and Applications to
Economics
Simultaneous Move Games
Games, contests, auctions, reputation, bargaining, indust
Strategic Interaction
First we introduced games and analyzed simultaneous-move games.
Econ 1870: Game Theory and Applications to
Economics
Sequential Move Games
We saw two solution concepts: iterated dominance and Nash
equilibrium.
Then we saw level k, a
Strategic Interaction
Econ 1870: Game Theory and Applications to
Economics
Games with Incomplete Information
So far weve introduced one-shot and repeated games with
simultaneous moves and sequential moves.
Weve seen the solution concepts iterated dominanc
Bayesian updating
Econ 1870: Game Theory and Applications to
Economics
More on PBE
Jim Campbell
Brown University
Spring 2015
Beliefs for P1: Pr (B|B or C ) =
Jim Campbell (Brown University)
More on PBE
Spring 2015
1/9
Bayesian updating
Jim Campbell (Brown
Thinking about thinking about strategies
Econ 1870: Game Theory and Applications to
Economics
Recursive Reasoning (part 2)
Last time we learned about level k reasoning
Its a nice behavioral story, but a bit vague
We saw already that predictions depend on
Econ 1870, Spring 2015
1
Problem Set 2: Level k and Sequential Games
Applying level k (20 points)
Unique NE is at (B, C).
L0
L1
L2
L3
L4
Row player Column player
Random
Random
B
R
M
C
B
L
B
C
At L4 each player is playing the same strategy as in the NE, an
V A N D E R B I L T U N I V E R S I T Y Department of Mathematics
Math 1111-01 FYWS The Mathematics of Games
Room: SC 1312 - Time: MWF 12:10p 1p
Fall, 2016 - 3 hours credit
Instructor: Dr. Lori Rafter
Office: SC 1232B
Office Phone: (34)3-1783
Math Office
ECON 1870, Spring 2013
Game Theory and Applications to Economics
Solutions to Problem Set 6
(30 points)
The set of players (bidders) is N = cfw_1, . . . , n, the set of actions for player i N is Ai = R+ , and player
i's type is denoted by vi Vi R. The bel
ECON 1870, Spring 2013
Game Theory and Applications to Economics
Solutions to Problem Set 5
Problem 1.
(15 pts) Player 1 is one of two dierent types, depending on which of the games is chosen by
T1 = cfw_G1, G2. His action space is A1 = cfw_T, B . A strat
Econ 1870: Game Theory and Applications
Problem Set 4 - Solutions
March 11, 2013
Problem 1. (20 points) 2.10 from Gibbons: (P1 , P2 ), (R1 , R2 ), (S1 , S2 ) are all Nash Equilibria, so no
matter what is played in the rst stage, no player wants to deviate
ECON 1870, Spring 2013
Game Theory and Applications to Economics
Problem Set 3 - Solutions
Problem 1
(30 points)
a. (5 points) There are 3 subgames: (1) the entire game, (2) the game that starts in the node where P2
moves having P1 played U, and (3) the g
ECON 1870 - Spring 2013, Problem Set 2 Solutions
(15 points)
Let p be the probability of player 1 playing T, and q be the probability of player 2 playing L.
Problem 1.
a. Pure-strategy NE: None
2
Mixed-strategy NE: p = 3 , q =
2
3
b. Pure-strategy NE: (T,
ECON 1870 - Spring 2013, Problem Set 1 Solutions
1. (10 points)
(a) (5 points) For player 1, B is dominated by T, so we can eliminate B. For player 2, C is dominated
by R, so we can eliminate C. No further elimination is possible. This leaves T and M for
Econ 1870 Spring 2013
Midterm Suggested Solutions
March 21, 2013
Part 1:
a) (5 points) False - a SPNE is a NE, but a NE is not necessarily subgame perfect.
P1
A
B
P2
C
P2
D
E
F
2
3
4
5
4
2
2
3
In this game, (B, DF) is a NE, but it is not subgame perfect.
ECON 1870 - Game Theory and Applications to Economics
Preparing for the Midterm
Georoy de Clippel
Brown University (Spring 2013)
Format The exam will start by asking you to dene some important concepts (see list below),
and then to solve exercises (compar
ECON 1870 - Game Theory and Applications to Economics
Georoy de Clippel
Brown University (Spring 2012)
Final Exam
Duration: 150 minutes. Total score: 95 points.
Permitted materials: non-programmable calculators, English and foreign language dictionaries.
Checklist of Basic Writing Principles
I.
Introduction
1. Do you have an attention-grabbing opening sentence?
2. Does the thesis refer to the main topic that was assigned?
3. Are the subtopics (supporting topic) addressed in the paper mentioned in the
intr
Thinking about thinking about strategies
The Nash equilibrium and iterated dominance solution concepts are
complicated in a couple of important ways.
Econ 1870: Game Theory and Applications to
Economics
Recursive Reasoning
First, in many interesting setti