Bargaining Games
Follow Osborne chapter 16
Game Theory
Dr. F. Fatemi
Graduate School of Management and Economics Sharif University of Technology
Page 262
Cooperative Games / Coalitional Games
This class of games focuses on strategic situations when action
In the Name of God
Sharif University of Technology
Graduate School of Management and Economics
Game Theory
44812 (1391-92 2nd term)
Dr. S. Farshad Fatemi
Introduction
Game: A situation in which intelligent decisions are necessarily
interdependent. A situa
Strict Nash Equilibrium
In a Nash equilibrium, a player might be indifferent between his
equilibrium action and some other action, given the action of the other
players.
Definition: The action profile in a strategic game is a Strict Nash
Equilibrium if f
Existence of Nash Equilibria
Before we can prove the existence, we need to remind you of the fixed
point theorem:
Kakutanis Fixed Point Theorem: Consider
set and a function
a compact convex
which has the following two properties:
i)
ii)
Then
Game Theory
Strict Dominance
Definition: For player a pure strategy
pure strategy
if and only if:
(
In this case,
strictly dominates another
)
(
)
is strictly dominated by
.
A strategy is strictly dominated if there is some strategy which strictly
dominates it.
must
Strategic Games with Imperfect Information
Lets start with an example (a different version of BoS):
= %50
1- = %50
Wife
Wife
Cinema
Husband
Theatre
Cinema
2,1
0,0
Theatre
0,0
1,2
Cinema
Theatre
Cinema
2,0
0,2
Theatre
0,1
1,0
Good day:
W wishes to meet H
Juries
What are the effects of different rules for juries?
a) Unanimity required for conviction (e.g. criminal trials in UK or US)
b) Only simple majority required (e.g. civil trials in UK)
Model jury decision making as a Bayesian game:
cfw_
Each juror h
Extensive Games with Perfect Information
A strategic situation in which players play a game over time.
At the point of making the decision, players are informed about the
action chosen before by the others.
It is also called Dynamic or Sequential-Move Gam
Sub-Game Perfect Equilibrium
Definition: A subgame of an extensive form game with complete
information is a subset of the game if it has the following properties:
1) It begins with a non terminal node (history)
2) Contains all the nodes that are successo
Extensive Games with Perfect Information
and Simultaneous Moves
In many cases, at some stages of the game (histories of the game)
players makes their decisions simultaneously.
One well documented example is repeated games where a
simultaneous game played
Repeated Games
Basic lesson of prisoners dilemma:
In one-shot interaction, individuals have incentive to behave
opportunistically
Leads to socially inefficient outcomes
In reality; some cases of prisoners dilemma end in cooperation
What happens if interac
Extensive Games with Imperfect Information
Definition (Os 314.1): An extensive game with imperfect
information consists of
a set of players
a set of terminal histories ; no sequence is a proper subhistory of
any other sequence
a player function
that co
Assignment # 1
Date 11/10/2016
Time:
12:30-02:00 PM
Total Mark:
5
Students Name
Students ID
Course Name
Introduction to Economics in English for NBS
Course Code
0308150 11E
Semester
Fall, 2016/2017
Instructors Name
Dr. Hasan Mustafa
Due date
20/10/2016
Qu