Lecture 5
Solution concepts
14.12 Game Theory
Muhamet Yildiz
Road Map
1. Dominant-strategy equilibrium
2. Rationalizability
3. Nash Equilibrium
1
Dominance
s-i =(s1, si-1,si+1,sn)
Definition: A pure strategy si* strictly
dominates si if and only if
u i
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. Dominance; dominant-strategy
equilibrium
1
Cardinal repre
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 write down a real number xi between 0
and 100 on a paper
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 is a nite set of players
Si is the set of pure strateg
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 equilibria will
not be stochastically stable.
1
General Pro
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,
and Pauzner)
Applications
2.
1.
2.
Currency attacks
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 parameter, e.g., whether income tax increases the
investment le
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 Complements
Dominance and equilibrium
Comparative statics
2
1
Two
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 try to maximize the expected value of
the von-Neumann a
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 of types for the sender; the realized type will be den
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 proper subgame is the original game, even if players obser
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. Suppose that each Si is a convex and compact subset of an Euc
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 nite set of players
Si is the set of pure strategies
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 Games
Normal-form/agent-normal-form
representations
Baye
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 concepts.
In order to analyze a game, we need to know
who
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 cannot choose two distinct alternatives at the same tim
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 analysis of the decision-making process
when there are more t