6.254 Game Theory with Engr App
Midterm Solutions
Thursday, April 8, 2010
Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexample. Exp
6.254 Game Theory with Engr App
Midterm
Thursday, April 8, 2010
Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexample. Explanations
6.254: Game Theory with Engr App
Project Description
As part of the requirements of the course, you need to complete a project on a topic of your choice, related to the class material. We encourage you to work in groups of 2-3 people. Please email Ermin i
6.254 Game Theory with Engineering Applications
Midterm April 8, 2008
Problem 1 : (35 points) Consider a game with two players, where the pure strategy of each player is given by xi [0, 1]. Assume that the payoff function ui of player i is given by ui (x1
6.254 Game Theory with Engineering Applications
Midterm April 11, 2006
Problem 1 : (35 points) Consider a Bertrand competition between two firms, where each firm chooses a price pi [0, 1]. Assume that one unit of demand is to be split between the two firm
6.972 Game Theory and Equilibrium Analysis
Midterm Exam April 6, 2004; 1-2:30 pm
Problem 1. (40 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexam
6.254: Game Theory with Engineering Applications February 23, 2010
Lecture 6: Continuous and Discontinuous Games
Lecturer: Asu Ozdaglar
1
Introduction
In this lecture, we will focus on: Existence of a mixed strategy Nash equilibrium for continuous games (
6.254: Game Theory
February 11, 2010
Lecture 4: Correlated Rationalizability
Lecturer: Asu Ozdaglar
1
Correlated Rationalizability
In this note, we allow a player to believe that the other players' actions are correlated- in other words, the other players
6.254 : Game Theory with Engineering Applications Lecture 20: Mechanism Design II
Asu Ozdaglar MIT
May 4, 2010
1
Game Theory: Lecture 20
Introduction
Outline
Mechanism design from social choice point of view Implementation in dominant strategies Revelatio
6.254 : Game Theory with Engineering Applications Lecture 19: Mechanism Design I
Asu Ozdaglar MIT
April 29, 2010
1
Game Theory: Lecture 19
Introduction
Outline
Mechanism design Revelation principle
Incentive compatibility Individual rationality
"Optimal"
6.254 : Game Theory with Engineering Applications Lecture 18: Games with Incomplete Information: Bayesian Nash Equilibria and Perfect Bayesian Equilibria
Asu Ozdaglar MIT
April 22, 2010
1
Game Theory: Lecture 18
Introduction
Outline
Bayesian Nash Equilibr
6.254 : Game Theory with Engineering Applications Lecture 17: Games with Incomplete Information: Bayesian Nash Equilibria
Asu Ozdaglar MIT
April 15, 2010
1
Game Theory: Lecture 17
Introduction
Outline
Incomplete information. Bayes rule and Bayesian infere
6.254 : Game Theory with Engineering Applications Lecture 16: Repeated Games II
Asu Ozdaglar MIT
April 13, 2010
1
Game Theory: Lecture 16
Introduction
Outline
Repeated Games perfect monitoring Folk Theorems Repeated Games imperfect monitoring
Price-trigge
6.254 : Game Theory with Engineering Applications Lecture 15: Repeated Games
Asu Ozdaglar MIT
April 1, 2010
1
Game Theory: Lecture 15
Introduction
Outline
Repeated Games (perfect monitoring)
The problem of cooperation Finitely-repeated prisoner's dilemma
6.254 : Game Theory with Engineering Applications Lecture 14: Nash Bargaining Solution
Asu Ozdaglar MIT
March 30, 2010
1
Game Theory: Lecture 14
Introduction
Outline
Rubinstein Bargaining Model with Alternating Offers Nash Bargaining Solution Relation of
6.254 : Game Theory with Engineering Applications Lecture 13: Extensive Form Games
Asu Ozdaglar MIT
March 18, 2010
1
Game Theory: Lecture 13
Introduction
Outline
Extensive Form Games with Perfect Information One-stage Deviation Principle Applications Ulti
6.254 : Game Theory with Engineering Applications Lecture 12: Extensive Form Games
Asu Ozdaglar MIT
March 16, 2010
1
Game Theory: Lecture 12
Introduction
Outline
Extensive Form Games with Perfect Information Backward Induction and Subgame Perfect Nash Equ
6.254 : Game Theory with Engineering Applications Lecture 11: Learning in Games
Asu Ozdaglar MIT
March 11, 2010
1
Game Theory: Lecture 11
Introduction
Outline
Learning in Games Fictitious Play Convergence of Fictitious Play
Reading: Fudenberg and Levine,
6.254 : Game Theory with Engineering Applications Lecture 10: Evolution and Learning in Games
Asu Ozdaglar MIT
March 9, 2010
1
Game Theory: Lecture 10
Introduction
Outline
Myopic and Rule of Thumb Behavior Evolution Evolutionarily Stable Strategies Replic
6.254 : Game Theory with Engineering Applications Lecture 9: Computation of NE in finite games
Asu Ozdaglar MIT
March 4, 2010
1
Game Theory: Lecture 9
Introduction
Introduction
In this lecture, we study various approaches for the computation of mixed Nash
6.254 : Game Theory with Engineering Applications Lecture 8: Supermodular and Potential Games
Asu Ozdaglar MIT
March 2, 2010
1
Game Theory: Lecture 8
Introduction
Outline
Review of Supermodular Games Potential Games Reading:
Fudenberg and Tirole, Section
6.254 : Game Theory with Engineering Applications Lecture 7: Supermodular Games
Asu Ozdaglar MIT
February 25, 2010
1
Game Theory: Lecture 7
Introduction
Outline
Uniqueness of a Pure Nash Equilibrium for Continuous Games Supermodular Games Reading:
Rosen J
6.254 : Game Theory with Engineering Applications Lecture 6: Continuous and Discontinuous Games
Asu Ozdaglar MIT
February 23, 2010
1
Game Theory: Lecture 6
Introduction
Outline
Continuous Games Existence of a Mixed Nash Equilibrium in Continuous Games (Gl
6.254 : Game Theory with Engineering Applications Lecture 5: Existence of a Nash Equilibrium
Asu Ozdaglar MIT
February 18, 2010
1
Game Theory: Lecture 5
Introduction
Outline
Pricing-Congestion Game Example Existence of a Mixed Strategy Nash Equilibrium in
6.254 : Game Theory with Engineering Applications Lecture 4: Strategic Form Games - Solution Concepts
Asu Ozdaglar MIT
February 11, 2010
1
Game Theory: Lecture 4
Introduction
Outline
Review Correlated Equilibrium Existence of a Mixed Strategy Equilibrium
6.254 : Game Theory with Engineering Applications Lecture 3: Strategic Form Games - Solution Concepts
Asu Ozdaglar MIT
February 9, 2010
1
Game Theory: Lecture 3
Introduction
Outline
Review Examples of Pure Strategy Nash Equilibria Mixed Strategies and Mix
6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games
Asu Ozdaglar MIT
February 4, 2009
1
Game Theory: Lecture 2
Introduction
Outline
Decisions, utility maximization Strategic form games Best responses and dominant strategies D
6.254 : Game Theory with Engineering Applications Lecture 1: Introduction
Asu Ozdaglar MIT
February 2, 2010
1
Game Theory: Lecture 1
Introduction
Optimization Theory: Optimize a single objective over a decision variable x Rn . i ui ( x ) subject to x X Rn
6.254: Game Theory with Engineering Applications Guest Lecture: Social Choice and Voting Theory
Daron Acemoglu MIT
May 6, 2010
1
Game Theory: Lecture 21
Introduction
Outline
Social choice and group decision-making Arrow' Impossibility Theorem s Gibbard-Sa
Tentative Syllabus
1. Introduction to Game Theory (1 Lecture): Games and solutions. Game theory and mechanism design. Examples from networks. 2. Strategic Form Games (4-5 Lectures): Matrix and continuous games. Iterated strict dominance. Rationalizability