Game Theory: Assignment #1
Due. March 23, 2014
Problem 1 [15 points]
Prove that any order of iterated deletion of strictly dominated strategy leads to a unique
subgame.1
Problem 2 [15 points]
Find two other examples2 that iterated deletion of weakly domin
Game Theory Lecture Notes Lecture 10
Hong Ma
Tsinghua University
Dec. 15, 2014
Nov. 27, 2015
Review: PD games - Coke War
Another example: How OPEC countries maintain high price for
their petro exports?
Coke War
I Pepsi and Coke are competing in price, the
Game Theory Homework 3
2016210557 Lu Xindi
October 11, 2016
1. Exercise 3.1
Problem:
Give the extensive and strategic forms of the game. Is it dominance solvable?
Solution:
(i) the extensive form of the game:
As indicated in Figure 1, Nature moves first a
Game Theory Homework 2
2016210557 Lu Xindi
October 7, 2016
1. Exercise 2.4
Solution:
As indicated in figure 1.14, dri /dqi < 0. Therefore, we have
2 ui
dri
q q
= 2i u j < 0.
i
dqi
q 2
i
Note that ui (qi , qj ) = qi p(qi + qj ) ci (qi ). Then we have
2 u
Game Theory Homework 4
2016210557 Lu Xindi
October 27, 2016
1. Exercise 6.3
Problem: Find an equilibrium in linear strategies.
Solution:
The optimal biding strategy
si (i ) = E[|0 6 6 i ]
Z i
1
=
p()d
P rob( 6 i ) 0
Z
1 i
=
1d
( U (0, 1)
i 0
i
= .
2
Both
Game Theory Homework 6
2016210557 Xindi Lu
October 30, 2016
Problem List: Exercise 7.2*
Problem: Inducing firms to reveal information about their cost of reducing their pollution.
1. Chapter 7, Exercise 7.2
Solution:
(a)Assume that the transfer takes the
Game Theory Homework 5
2016210557 Xindi Lu
November 1, 2016
Problem List: Exercise 7.1*
Problem: Solve for the optimal symmetric auction.
1. Chapter 7, Exercise 7.1
Solution:
The sellers expected profit is given by
Eu0 = p(XW + (1 X)L) + p(XW + (1 X)L),
w
GAME THEORY
Game Theory = Interactive Decision Theory
2
Games We Play
3
Games Businesses Play
4
Why Study Game Theory?
5
A Game
6
A Game
7
1 is rational
2 is rational and knows that 1 is rational
A Coordination Game
8
A Coordination Game
9
Battle of Se
GAME THEORY
Road Map
2
Backward induction
Sequential bargainning - Pretrial negotiation
Subgame perfect equilibrium
Battle of the sexes with outside option
Bank runs
Single-deviation principle - infinite horizon bargaining
Finitely repeated games
Inf
Let x be the probability player 1 plays U and let y be the probability player 2 plays L.
(i)
The utilities for player 1 is computed as follows:
1 () = + (1 ),
1 () = + (1 ).
Therefore, player 1s reaction function 1 () satisfies
( = 1)
1 () = cfw_
( = 0)
Administrative Issues
Course Policy
ext books
Required: Game theory,
Fudenberg and Tirole, MIT press.
1991.
Reference: (1) Game Theory, R. B. Myerson, Harvard University
Press. 1991. (2) The Art of Strategy: A Game Theorist's Guide
to Success in Busines
Game Theory Lecture Notes Lecture 8
Hong Ma
Tsinghua University
Nov. 13, 2015
AGENDA
I
Rubinstein Bargaining: alternating Oers Bargaining with
innite horizon
I
(Osborne, Chap. 16)
I
Nash Bargaining
I
Mechanism design: fair division (optional)
I
Repeated G
Game Theory Lecture Notes Lecture 11
Hong Ma
Tsinghua University
Dec. 04, 2015
Games with Incomplete Information
Or as in Osborne textbook, games with imperfect
information.
I
Now we introduce information asymmetry into our analysis.
I
Some players have i
Game Theory Lecture Notes Lecture 9
Hong Ma
Tsinghua University
Nov. 20, 2015
Agenda
I
Repeated Games: Concepts
I
I
discount factor
trigger strategies
I
Repeated Games: Applications
I
Note: Homework 4 posted online
Discounted Sum
I
For an innite sequence
Game Theory
Lecture 4: Incomplete Information Game
Game of Coins in the Jar
Game Theory and Behavioral Decision Making
2
Incomplete Information
In many real world game situations, a player does not know the
payoffs or preference of others.
Real world si
Game Theory
Lecture 2: Iterated Strict Dominance,
Rationalizability, and Mixed Strategy Nash
Equilibrium
Review of the Last Class
Strategic-form game Simultaneous move
Dominated strategies never be played
Nash equilibrium (pure strategy profile)
Best res
Game Theory
Lecture 5: Mechanism Design
Part I: Discrete Types
Summary of Bayesian NE
Second Price Auction Game
Game Theory and Behavioral Decision Making
2
Mechanism Design Introduction
Mechanism design is a special class of incomplete inform
ation gam
Game Theory
Lecture 1: Introduction
Decision Theory and Game Theory
Optimal
decision model: Optimize a single objective ov
er decision variable.
Game theory: study the decisions in a strategic situati
on where a decision makers objective depends on no
t o
Game Theory
Lecture 3: Extensive Form Game and
Subgame Perfect Equilibrium
A Game of Cash in the Envelope
Player 1 can put 0$, 10$, or 30$ in an Envelope. Then
the envelope is passed to player 2.
Player 2 can either match (i.e. add the same amoun
t) or po
Homework 3
1. There are n firms.
First, simultaneously each firm decides whether to enter a market, by incurring a
cost C. (If a firm does not enter, its payoff is 0.)
Then, knowing which firms entered, each firm i in the market simultaneously
produces qi
Consider the following twoplayer game in extensive form.
(a) Write this game in normal form.
(b) Find all the rationalizable strategies.
(3) Find all Nash equilibria in pure strategies.
(d) Iteratively eliminate all the weakly dominated strategies.
First-Price
First-Price and Dutch
Theorem
First-Price and Dutch auctions are strategically equivalent.
In both rst-price and Dutch, a bidder must decide on the
amount hes willing to pay, conditional on having placed the
highest bid.
despite the fact that
Revenue Equivalence
Revenue Equivalence
Which auction should an auctioneer choose? To some extent,
it doesnt matter.
Theorem (Revenue Equivalence Theorem)
Assume that each of n risk-neutral agents has an independent
private valuation for a single good at
Game Theory
Taught by Prof. Pingzhong Tang
Spring 2013
Final Exam
06/23/13
Time Limit: 2 Hours
Name (Print):
Student ID:
This exam contains 2 pages (including this cover page) and 4 problems. Check to see if any
pages are missing. Enter all requested info
3 Game Theory II: Sequential-Move and
Repeated Games
Recognizing that the contributions you make to a shared computer cluster today
will be known to other participants tomorrow, you wonder how that aects how
many resources you should contribute. What if o
Lecture XV: Games with Incomplete
Information
Markus M. Mbius
o
April 20, 2007
Osborne, chapter 9
Gibbons, chapter 3
1
Introduction
Informally, a game with incomplete information is a game where the game
being played is not common knowledge. This idea i