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ECON1401 topic 1 Game theory lecture 1
28/02/2011
1
ECON 1401: Economic Analysis
Topic 1: Game theory
Gautam Bose
Lecture 1
Games and their solutions
Today’s Agenda
•
What is a game, and what is “game theory”?
•
Simultaneous Games and Their Solution Concepts
The game matrix (game table)
g
(g
)
•
Examples.
–
Nash equilibrium
–
multiple equilibria
•
Sequential Games and Their Solution Concepts
ECON1401 Semester 1 2011 Lecture
22
–
How to write down and solve a Sequential Game.
–
Rollback (subgame
‐
perfect) equilibrium.
–
Examples.
Game Theory
•
Game theory is a unified method for analysing
rategic interactive situations which span the
strategic, interactive situations which span the
spectrum from tic
‐
tac
‐
toe to nuclear arms races.
•
It is a “theory” because it abstracts the essential,
common features of these situations, and
analyses them in the abstract.
•
use game
‐
eoretic insights and shed light on
ECON 1401 Semester 1 2011 Lecture
23
To use game theoretic insights and shed light on
a
particular
situation (e.g. enterprise bargaining
at UNSW), we have to colour in the specific
details.
Games
•
What is a game?
–
A situation involving two or more agents (“players”)
hite and black in chess
•
White and black in chess
•
Management vs union
•
Obama and the Republican challenger
–
Each of whom can adopt one of several permissible
courses of action (“strategies”)
•
Mgmt offers small/medium/large pay rise, union threatens
strike if demands are not met (other strategies)
ECON 1401 Semester 1 2011 Lecture
24
(
g)
–
The combination of strategies together determine the
outcome for each player (“payoffs”)
•
Medium pay raise for union, little work loss combined with
high worker morale for management (other outcomes)
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View Full DocumentECON1401 topic 1 Game theory lecture 1
28/02/2011
2
Simultaneous and sequential games
•
In some games, all players choose their actions
the same time (without knowing the
at the same time (without knowing the
choices of other players).
–
sealed
‐
bid auction, or tender
–
Scissors, paper, rock
•
In other games, there is a given sequence in
which players choose their actions/strategies.
ECON 1401 Semester 1 2011 Lecture
25
–
Bargaining over a price (offer
‐
counteroffer)
–
Tic
‐
tac
‐
toe and chess
•
Different analysis for the two kinds of games
What do we want to determine?
•
Given the specifications of a game, how will the
players play?
•
This cannot usually be answered for one player in
isolation, because the best that one can do
depends on what the other does.
•
The test of whether a player has done the best is
that the player does not
in retrospect
wish she
ad done something
ifferent
ECON 1401 Semester 1 2011 Lecture
26
had done something different.
•
If we can find an outcome in which this criterion
is satisfied for each player, we have found an
equilibrium
.
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