ECON 110: Game Theory in the Social Sciences
HW#5 KEY: Due date Wednesday August 10th 2016
1) Consider a first-price, sealed-bid auction in which a bidders valuation
can take one of three values: 5, 7, and 10, occurring with probabilities .2,
.5, and .3,
Natalia Garbiras D
az
Econ 110 PS 135
Section Notes (105 and 106)
Section 2, Fall 2015
September 9, 2015
Before starting.
1. Problem set submission:
Problem sets must be submitted during the last 5 minutes of the lecture in the Hall outside 245 Li Ka
Shin
Fall 2013
GAME THEORY IN THE SOCIAL SCIENCES
Problem Set 3
(Due at the start of Lecture Thursday, October 17)
Question 1 (from the F2010 midterm but somehow still seems timely): It is January 2011 and
the midterm elections are over. A new Congress has beg
Fall 2013
GAME THEORY IN THE SOCIAL SCIENCES
Problem Set 3
(Due at the start of Lecture Thursday, October 17)
Question 1 (from the F2010 midterm but somehow still seems timely): It is January 2011 and
the midterm elections are over. A new Congress has beg
Outline for today
Stat155
Game Theory
Lecture 10: More on von Neumanns Minimax Theorem
von Neumanns minimax theorem
Low regret learning algorithms for playing games.
Series and parallel games.
Peter Bartlett
September 27, 2016
1 / 21
von Neumanns Minimax
Outline for today
Stat155
Game Theory
Lecture 23: Shapley value
Multi-player transferable utility cooperative games
Recall: Characteristic function, Gillies core
Shapleys axioms
Shapleys Theorem
Examples
Peter Bartlett
November 17, 2016
1 / 20
Recall: Mul
Outline for today
Stat155
Game Theory
Lecture 19: Price of anarchy. Cooperative games.
Price of anarchy
Recall: Linear and affine latencies
Classes of latencies
Pigou networks
Peter Bartlett
Cooperative games
Transferable versus nontransferable utility
No
Statistics 155 Homework Assignment 3 (due Thursday, September 22, 2016)
1. (A drinking game) Ferguson, Exercise 1.5 (4), pII-8.
The entertaining book The Compleat Strategyst by John Williams contains many simple examples and
informative discussion of stra
Outline for today
Stat155
Game Theory
Lecture 24: Shapley value. Voting systems.
Shapley value
Recall: Shapleys Theorem
Examples
Designing games
Peter Bartlett
Voting systems.
November 22, 2016
1 / 23
2 / 23
Recall: Multiplayer TU cooperative games
Shaple
Outline for today
Stat155
Game Theory
Lecture 22: Nash bargaining.
Multiplayer TU cooperative games.
Two-player nontransferable utility cooperative games
Bargaining problems
Nashs bargaining axioms
The Nash bargaining solution
Multi-player transferable ut
Chapter: Repeated
Games
Econ 110
Repeated Game
Players interact many time over the
course of the game.
Intuition in solving the game: If
players believe that the nature of current
interaction affects future behavior, they
may change their current behavi
Outline for today
Stat155
Game Theory
Lecture 26: More Voting.
Voting systems.
Recall: voting and ranking rules, Arrows impossibility theorem
Voting rules: Gibbard-Satterthwaite Theorem
Properties of voting rules
Properties of instant runoff voting
Borda
Outline for today
Stat155
Game Theory
Lecture 8: Symmetry in two player zero-sum games
Solving two player zero-sum games
Recall: definitions, solving 2 2, 2 n and m 2 games, principle of
indifference
Symmetry
Peter Bartlett
Invariance of payoffs under per
Outline for today
Stat155
Game Theory
Lecture 20: Cooperative games, transferable utility
Transferable utility cooperative games
Cooperative strategy
Threat strategies, disagreement point
Final payoff vector
Nontransferable utility cooperative games
Peter
Outline for today
Stat155
Game Theory
Lecture 14: General-Sum Games
Multiplayer general-sum games
Definitions: utility functions, Nash equilibria.
Nashs Theorem
Congestion games and potential games
Congestion games
Every congestion game has a pure Nash eq
Solutions to some Chapter 13 exercises
13.1 See Lecture 26, slide 22.
13.3 Instant run-off voting and plurality voting. See Lecture 25, slide 17.
13.4 See p367.
13.5 Plurality and Borda count are positional voting methods. To prove consistency, well show
Outline for today
Stat155
Game Theory
Lecture 9: von Neumanns Minimax Theorem
Nash equilibrium.
Games as linear programs.
von Neumanns minimax theorem
Peter Bartlett
Low regret learning algorithms for playing games.
September 22, 2016
1 / 20
Recall: Saddl
Game Theory in the
Social Sciences
Econ 110
Contacting Me
The best way to get in touch with me is by
email [email protected]
In order to ensure that I dont accidentally
delete your emails, please put Econ 10 in
the subject.
Office Hours
Tuesday a
NAME_
ECON 110: Game Theory in the Social Sciences
HW#1: Due date Thursday June 30th 2016
1)
Suppose that Speedy Bike and Power Bike are the only two bicycle manufacturing firms serving the
market. Both can choose large or small advertising budgets. Assum
ECON 110: Game Theory in the Social Sciences
HW#2 KEY: Due date Wednesday July 6th 2016
1) Suppose that two identical firms produce widgets and that they are the only firms in
the market. Their costs are given by C1 10Q1 and C2 10Q2, where Q1 is the outpu
Chapter 6: An
Application
Cournot Duopoly
Econ 110
Classification of Market
Market classification based on number of sellers:
Two extreme cases
(i) Monopoly (one seller)
(ii) Pure Competition (Many many seller)
Both are extensively studied and both c
ECON 110: Game Theory in the Social Sciences
HW#4 KEY: Due date Thursday August 4th 2016
1) Greg is deciding whether to ask Marcia out on a date. However, Greg isnt sure whether Marcia likes
him, and he would rather not ask if he expects to be rejected. W
Chapter: An Application of
Backward Induction to
Research and Development
Econ 110
Introduction
Major source of economic growth
Technological Advances
Some studies show that up to 87% of economic
growth is a result of technological advances
What drive
ECON 110: Game Theory in the Social Sciences
HW#3 KEY: Due date Thursday July 21st 2016
1) Consider the following extensive form game.
a) Number of subgames are _4_
b) SPNE in the following game is (Show your paths of equilibrium on each subgame on the ex
Chapter: Incomplete
Information Games
Econ 110
Incomplete Information Vs Imperfect Information Game
Incomplete information games are not same as imperfect
information games.
Imperfect information games: Players know what game
they are playingbut at some
NAME_
ECON 110: Game Theory in the Social Sciences
HW#2: Due date Wednesday July 6th 2016
1) Suppose that two identical firms produce widgets and that they are the only firms in
the market. Their costs are given by C1 10Q1 and C2 10Q2, where Q1 is the out
Spring 2017 Stat 155 :Game Theory
Lecture 1
Introduction and Course Overview, PBICG
Shobhana Stoyanov
Department of Statistics
UC Berkeley
January 18, 2017
Shobhana Stoyanov
Spring 2017 Stat 155 :Game Theory Lecture 1 Introduction and Course Overview,
Cou
Final Exam
Stat155
Game Theory
Lecture 27: Final Review
This is an open book exam: you can use any printed or written material,
but you cannot use a laptop, tablet, or phone (or any device that can
communicate). Answer each question in the space provided.
Stat155 Final Exam (December 13, 2016) Solutions
1. Consider the following combinatorial game, which we call circular Nim:
Thirty coins are placed in three circles, with ten coins in each circle and each coin touching
its two neighboring coins. At each mo
Outline for today
Stat155
Game Theory
Lecture 15: Evolutionary game theory
Nash equilibria
Criticisms of Nash equilibria
Example: hawks and doves
Peter Bartlett
Evolutionarily stable strategies
October 18, 2016
1 / 21
2 / 21
Multiplayer general-sum games
Outline for today
Stat155
Game Theory
Lecture 18: The price of anarchy
Price of anarchy
Recall: Braesss paradox
Price of anarchy
Nash equilibrium flows exist
Linear latency
Affine latency
The impact of adding edges
Peter Bartlett
October 27, 2016
1 / 21
B
Outline for today
Stat155
Game Theory
Lecture 17: Correlated equilibria and the price of anarchy
Peter Bartlett
Correlated equilibrium
Example: traffic signals
Definitions
CE vs NE
Price of anarchy
Example: Braesss paradox
October 25, 2016
2 / 17
1 / 17
A