ECON 421: Problem Set 4
Vitor Farinha Luz
Due on Friday, December 2nd, at 5pm. You can either hand in the problem set on the TA review session
or in my oce (Iona 203). If you wont be on campus, please email me a scanned version of your problem
set. No lat
ECON 421: Problem Set 3
Vitor Farinha Luz
November 3, 2016
Due on Monday, November 14th, in the TA Oce hour (6pm). Make sure to hand it in before due date
if you cannot make it to the oce hour. No late problem sets will be accepted.
Always show the calcul
ECON 421: Problem Set 2
October 21, 2016
Professor: Vitor Farinha Luz
Due on November 1st in the beginning of class. No late problem sets will be accepted.
Always show the calculations leading to your final answer.
Question 1) Consider the following exten
ECON 421: Problem Set 1
October 2, 2016
Professor: Vitor Farinha Luz
Due on October 4th at 5pm. You can slide the problem set unde rmy oce door if I am
not in. No late problem sets will be accepted.
Always show the calculations leading to your final answe
10/4/16
University of British Columbia, VSE
Econ 421: Topic II
Extensive Form Games and
Subgame Perfect Equilibrium
2016-2017, Term 1
Professor Vitor Farinha Luz
Email: [email protected]
Office: Iona 203
Office hours: Tuesdays 5-6:30pm
Roadmap
Desc
ECON 421: Introduction to Game Theory and
Applications
Instructor: Vitor Farinha Luz
Email: [email protected]
1
Description:
This course covers principles of rational behavior in strategic situations and various notions
of equilibrium useful in pred
VSE, University of British Columbia
Econ 421
Strategic (normal) form games
2016-2017, Term 1
Professor Vitor Farinha Luz
Email: [email protected]
Office: Iona 203
Office hours: Tuesdays 5-6:30pm
Announcements
Office hours:
Monday 11-12:30pm
Iona
Solutions Problem set 1
October 6, 2016
Question 1.
a) This game has three Nash equilibria: (U, l, X), (U, r, X) and (D, l, Y ).
b) In this game no player has a strictly dominated action. Hence we have that
Ii0 = Ii1 = Ai ,
which means that Ii = Ai for al
ECON 421: Introduction to Game Theory and Applications
In-class Midterm 1, 2015
October 8th, 2015
INSTRUCTIONS:
Midterm 1 has seven questions and a total of 150 points. You have 75 minutes to
complete it.
Please write all your final answers on the bookl
11/14/2013
University of British Columbia
Department of Economics
Econ 421: Topic III
Games of incomplete information:
Dynamic games
Professor Wei Li
Phone: (604) 822-2839
Email: [email protected]
Office: 1015 Buchanan Tower
Office hours: T: 1-2pm and Th: 2-3
Application: information in voting
States: A and B, e.g., war and peace
Two candidates: 1 and 2 (hawk vs. dove party)
Voters a and b have identical preferences
Both voters payoffs are 1 if the right
voters
candidate wins (1 wins in state A or 2 wins in
11/19/2013
Signaling toughness: beer & quiche
Prior to the entry decision, the incumbent gets
to choose a breakfast.
An incumbent facing a potential entrant
Incumbent gets 4 if the entrant stays out, and 2 if
the entrant enters.
Entrant gets 2 if she
11/26/2013
Strategic communication
(costless signaling)
Signaling is costly, but costs different for
different types
What if there is no cost?
Talk is cheap. Or is it?
Depends on the alignment of interest
between the sender and the receiver
Some info
10/24/2013
What can be achieved in the long
term?
Repeated games are used to model ideas like
social norms, customs;
threats, punishments and revenge.
Players can achieve a larger set of payoffs in
repeated games.
But what payoffs can be achieved in
Application: price competition
Two workhorse models: quantity (Cournot)
competition and price (Bertrand) competition.
In price competition, there are N = cfw_1,2 firms.
Simultaneously each firm i sets a price pi;
Simultaneously,
If pi < pj, firm i sel
University of British Columbia
Department of Economics
Econ 421: Topic III
Static games of incomplete information
Professor Wei Li
Phone: (604) 822-2839
Email: [email protected]
Office: 1015 Buchanan Tower
Office hours: T: 1-2pm and Th: 2-3pm
Incomplete infor
9/30/2013
University of British Columbia
Department of Economics
Econ 421: Topic II
Extensive Form Games and
Subgame Perfect Equilibrium
Professor Wei Li
Phone: (604) 822-2839
Email: [email protected]
Office: 1015 Buchanan Tower
Office hours: T: 1-2pm and Th:
10/22/2013
Two Trigger Strategies in PD game
1. Grim Trigger Strategy
Cooperate until a rival deviates
Once a deviation occurs, play noncooperatively for the rest of the game
p
y
g
2. Tit-for-Tat Strategy
Cooperate if your rival cooperated in the
most
Mixed strategy
Pure strategy: all the eggs in
one basket.
Anyone for tennis?
Serve left or right?
g
Penalty kicks in soccer.
Randomize surprise the
rival.
Matching pennies
2
1
Head
Tail
Head (1,-1) (-1,1)
H d (1 1) ( 1 1)
Tail
(-1,1) (1,-1)
No pure
10/15/2013
Repeated games
University of British Columbia
Department of Economics
A special case of extensive form games: the
same stage game is played again and again
Econ 421: Extensive Form Games
Part II: Repeated Games
Two types of repeated games:
F
10/8/2013
Subgame Perfect Equilibrium (SPE)
Subgames: (counter)examples
1. Subgame: in any given game, there may be
some smaller games embedded.
2. A subgame must:
Begin at a singleton node;
Include all the nodes and branches that come
after;
But do no
University of British Columbia
Department of Economics
Econ 421: Introduction to
Game Theory and Applications
2013-2014, Term 1
Professor Wei Li
Phone: (604) 822-2839
Email: [email protected]
Office: 1015 Buchanan Tower
Office hours: Tuesdays: 1-2pm
Thursdays
University of British Columbia
Department of Economics
Econ 421: Introduction to
Game Theory and Applications
2013-2014, Term 1
Professor Wei Li
Phone: (604) 822-2839
Email: [email protected]
Office: 1015 Buchanan Tower
Office hours: Tuesdays: 1-2pm
Thursdays
The strategic environment
Payoffs: numbers associated with each possible
outcome, which depends on all players actions
Expected payoffs if outcomes are random
Example: other regarding preferences
Rules of the game
Timing of moves
What is the order of
University of British Columbia
Department of Economics
Econ 421: Problem Set 3
Professor Wei Li
Phone: 2-2839
Posted on Thursday, November 14, due back on 4pm Tuesday, Dec. 3. No late problem
set accepted.
Problem set 3 has a total of 100 points distrib
University of British Columbia
Department of Economics
Econ 421: Problem Set 1
Professor Wei Li
Phone: 2-2839
Posted on Tuesday, September 17, due back in class on Thursday, October 3.
No late problem set accepted.
Problem set 1 has a total of 100 point
University of British Columbia
Department of Economics
Econ 421: Problem Set 2
Professor Wei Li
Phone: 2-2839
Posted on Thursday, October 17, due back in class on Thursday, November 7. No late
problem set accepted.
Problem set 2 has a total of 100 point