Network Economics and Game Theory Homework 1
Prepared by Mihaela van der Schaar and Yuanzhang Xiao
Please bring the problem at the beginning of class (4pm) on Jan. 26, 2015
1. (Iterative dominance)
Use iterative dominance to find the pure Nash equilibrium
Homework 1 - Solutions
1. Find or create examples of 2-by-2 games with the following properties:
(a) No pure Nash equilibrium.
(b) No weakly Pareto-dominant strategy profile.
(c) At least two Nash equilibria, including one equilibrium that Pareto-dominate
Network Economics and Game Theory Homework 1
Prepared by Mihaela van der Schaar
Please send your homework before Jan. 23 at 12pm by email to
Mr. Linqi Song (TA) at:
[email protected]
For inquiries about the homework, please contact the instructor.
1. Iden
Course name: EE 218 - Network Economics and Game Theory
Instructor: Prof. Mihaela van der Schaar (email: [email protected])
Brief Description:
This course introduces basic as well as advanced microeconomics, game theory and strategic design
concep
Homework 5
1. Roy and Siegfried live on a small island off the cost of the state of Maine. They
want to build a bridge to the island, which will cost 5 (hundred thousand dollars) but
they cannot decide how the cost should be divided between them. Only Roy
Solution to Homework 4
1. Bayesian perfect and sequential equilibria
Consider the following game played by two parties, A and B. First, nature chooses either C or
D. C is chosen with probability 0.7, and D is chosen with probability 0.3. Second, party A c
Network Economics and Game Theory Homework 1
Prepared by Mihaela van der Schaar and Jie Xu (TA)
Please send your homework before Jan. 24 at 12pm by email to Jie at:
[email protected]
For inquiries about the homework, please contact either the instructor
EE218: Network Economics and Game Theory
Prof. Mihaela van der Schaar
Name:
Winter 2014
Student ID:
MIDTERM EXAMINATION
(Open Book, No electronic devices)
1
1. Consider the following game in normal form, where player 1 chooses rows and player 2 chooses co
EE 218 HW #5
Problem 1. (Mediation)
ROW and COL are engaged in a contact dispute. They agree that COL owes
money to ROW, but they disagree about how much. If they go to court, the
outcome will depend on how strong each case is; the table below shows how
m
Lecture 3
Ongoing interactions:
Dynamic games of
complete information
- Part 1
Outline
Extensive-form games
Interventions: Policing, treats, punishments
Repeated games formalism, equilibria, automata
Direct vs. Indirect Reciprocity
Sub-game perfect equili
Lecture 3
Dynamic games of complete information
- Part 2
Outline (part 2)
Repeated games
Finite
Infinite
Questions/comments/observations are always
encouraged, at any point during the lecture!
Motivation
Play the same normal-form game over and over
each r
Lecture 2
Non-cooperative game theory in
networks and systems One shot interactions
Two branches of game theory
Noncooperative game theory
Players maximize their payoffs independently given their
knowledge about the game.
Solution concepts: Nash equilibri
Lecture 3
Dynamic games of complete information
- Part 2
Outline (part 2)
Repeated games
Finite
Infinite
Questions/comments/observations are always
encouraged, at any point during the lecture!
Motivation
Play the same normal-form game over and over
each r
EE 218:
Network economics
and game theory
Prof. Mihaela van der Schaar
email: [email protected]
http:/medianetlab.ee.ucla.edu/
Lecture 1
Strategic interactions in networks and
systems a motivation
Outline
Why should engineers care about game theory?
Why
Network Economics and Game Theory Homework 1
Prepared by Mihaela van der Schaar and Kartik Ahuja
1. (Iterative dominance)
Use iterative dominance to find the pure Nash equilibrium in the game shown in the following table.
Table 1. A three-by-three game
U
Lecture "6$5*0/4
1
One seller/many buyers
n + 1 players N = cfw_0, 1, . . . , N
seller = 0 ; B = cfw_1, . . . , N = buyers
Types T0 = cfw_0; Ti [0, 1)
probability distribution on [0, 1)n
Decisions: (, z)
probability distribution over N (who gets it
EE218 - Network economics
and game theory
What have we learned this quarter?
A brief review
Multi-agent systems
Connected, self-interested, intelligent, learning entities
(people, machines, software )
social cloud computing, social networks, expert networ
EE-218 Networks Economics and Game Theory
Homework 4
Consider there is 1 Seller, 1 Buyer, 1 Car. The car is either High quality H or Low quality L. Valuations
are: VSeller ( H ) = 4 , Vseller ( L) = 1 , Vbuyer ( H ) = 6 , Vbuyer ( L) = 3 .
It is common kn
1: Games & Equilibrium: Rationality vs E
(John Nash)
ciency
2: Repeated Games: Cooperation/Collusion in the Long Run
(Robert Aumann)
3: Bayesian Games & Mechanism Design: Limits of the Possible
(John Harsanyi; Leonid Hurwicz, Eric Maskin, Roger Myerson)
1
Repeated Games: Ingredients
Stage game
players
actions for
player
profile of actions
of all players
utility of player
Repeated Games: Time, Information
Time
In period
(discrete)
G is played
players know what happened before (history)
players choose actio
Lecture 6 Part 2
Mechanism Design
Incentive engineering
Outline
Motivation and examples
Mechanism Design Principles
Efficient mechanisms
Applications to resource allocations in networks and
systems
Auctions requirements, design, principles
Applications to
Network economics and game theory Midterm exam 2011
1. Infinitely Repeated Prisoners Dilemma
Consider the Prisoners dilemma game with the following payoffs:
2
C
D
C
(4, 4)
(1, 6)
D
(6, 1)
(2, 2)
1
Suppose that the game is going to be repeated forever. Sup
EE218: Network Economics and Game Theory
Prof. Mihaela van der Schaar
Name:
Winter 2013
Student ID:
MIDTERM EXAMINATION
(Open Book, No electronic devices)
1
1. In the following game, ROW chooses the row to be played, COL chooses the column to be played,
M
Homework 2. Conjectural equilibrium
Consider the following two-user game with utility functions
2
u1 a1,a2 a1 3 a1 a2 , u2 a1,a2 a2 3 a1 a2 ,
in which ai represents the action of user i and a1, a2 0 .
(a) Derive the best response function BRi ai for given
Solution to Homework 3
1. Ultimatum Game
Let us consider the following ultimatum game: There is $5 to divide. Player 1 offers a division
strictly positive whole numbers of dollars so not ($5, $0) or ($4.5, $0.5) player 2 accepts or
rejects. If player 2 a
Homework 5
1. Roy and Siegfried live on a small island off the cost of the state of Maine. They
want to build a bridge to the island, which will cost 5 (hundred thousand dollars) but
they cannot decide how the cost should be divided between them. Only Roy
EE 218B HW #6
Problem 1. (Mediation)
ROW and COL are engaged in a contact dispute. They agree that COL owes
money to ROW, but they disagree about how much. If they go to court, the
outcome will depend on how strong each case is; the table below shows how
Homework 4
EE218 Network Economics and Game Theory
This homework will be due at the beginning of the class (4pm) on Monday, Feb. 23
Please bring this homework printed. Please DO NOT send this homework via email to the
instructor or to the TA. The instruct
Network Economics and Game Theory Homework 3
1. Infinitely Repeated Prisoners Dilemma
Consider the Prisoners dilemma game. Specifically, the following game is going to be played
repeatedly:
2
C
D
C
(5, 5)
(0, 6)
D
(6, 0)
(4, 4)
1
Suppose that the game is
Mechanism Theory
Matthew O. Jackson
Humanities and Social Sciences 228-77, California Institute of Technology
Pasadena, California 91125, U.S.A.
October 12, 2000, revised December 8, 2003
An abridged version of this appears in Optimization and Operations