Lecture 7
Mixed-Strategy Nash Equilibrium
14.12 Game Theory
Muhamet Yildiz
Road Map
1.
2.
3.
4.
Some 2x2 games
Mixed-strategy Nash Equilibrium
Quiz
Applications and examples:
1. Price competition with
Lecture 3
Representation of Games
14.12 Game Theory
Muhamet Yildiz
Road Map
1. Cardinal representation Expected
utility theory
2. Quiz
3. Representation of games in strategic
and extensive forms
4. Do
14.12 Economic Applications of
Game Theory
Professor: Muhamet Yildiz
Lecture: MW 3:00-4:30
1
Recitations
F 10
F 3
F xx (xxx)
Quiz Problem
Without discussing with anyone, each student
is to w
NON-COOPERATIVE GAMES
MIHAI MANEA
Department of Economics, MIT,
1. Normal-Form Games
A normal (or strategic) form game is a triplet (N, S, U ) with the following properties
N = cfw_1, 2, . . . , n i
LearningAdjustment with
persistent noise
14.126 Game Theory
Mihai Manea
Muhamet Yildiz
Main idea
There will always be small but positive
probability of mutation.
Then, some of the strict Nash equili
Global Games
14.126 Game Theory
Muhamet Yildiz
Road map
Theory
1.
1.
2.
3.
2 x 2 Games (Carlsson and van Damme)
Continuum of players (Morris and Shin)
General supermodular games (Frankel, Morris,
14.126 Lecture Notes on Supermodular Games
Muhamet Yildiz
April 22, 2010
A common exercise in economics is to understand how a particular outcome varies
qualitatively varies with a particular paramete
Supermodularity
14. 126 Game Theory
Muhamet Yildiz
Based on Lectures by Paul Milgrom
1
Road Map
Definitions: lattices, set orders, supermodularity
Optimization problems
Games with Strategic Complement
14.126 Lecture Notes on Rationalizability
Muhamet Yildiz
April 9, 2010
When we dene a game we implicitly assume that the structure (i.e. the set of players, their strategy sets and the fact that they
14.126 GAME THEORY
MIHAI MANEA
Department of Economics, MIT,
1. Forward Induction in Signaling Games
Consider now a signaling game. There are two players, a sender S and a receiver R.
There is a set T
14.126 GAME THEORY
MIHAI MANEA
Department of Economics, MIT,
1. Sequential Equilibrium
In multi-stage games with incomplete information, say where payos depend on initial
moves by nature, the only pro
14.126 GAME THEORY
MIHAI MANEA
Department of Economics, MIT,
1. Existence and Continuity of Nash Equilibria
Follow Muhamets slides. We need the following result for future reference.
Theorem 1. Suppos
14.126 GAME THEORY
MIHAI MANEA
Department of Economics, MIT,
1. Normal-Form Games
A normal (or strategic) form game is a triplet (N, S, U ) with the following properties
N = cfw_1, 2, . . . , n is a
Review of Basic Concepts:
Normal form
14.126 Game Theory
Muhamet Yildiz
Road Map
Normal-form Games
Dominance & Rationalizability
Nash Equilibrium
Existence and continuity properties
Bayesian Game
14.12 Game Theory Lecture Notes
Lectures 3-6
Muhamet Yildiz
We will formally dene the games and some solution concepts, such as Nash Equilibrium, and discuss the assumptions behind these solution conc
14.12 Game Theory Lecture Notes
Theory of Choice
Muhamet Yildiz
(Lecture 2)
1
The basic theory of choice
We consider a set X of alternatives. Alternatives are mutually exclusive in the sense
that one
14.12 Game Theory Lecture Notes
Introduction
Muhamet Yildiz
(Lecture 1)
Game Theory is a misnomer for Multiperson Decision Theory. It develops tools,
methods, and language that allow a coherent analys