Bargaining
McGill University
Econ 546
H AGGLING AND ITS VARIANTS
The price of vegetables at the local vendor.
Salary of CFL players
Divorce settlements
International border disputes
Trade unions and r
Extensive Games with Imperfect Information
McGill University
Econ 546
E XTENSIVE G AMES
Set of players.
Set of information sets. (who moves when)
For each player and for every information set when the
Signaling
McGill University
Econ 546
S IGNALING GAMES
Two players, Sender and Receiver.
Receiver needs to take an action that affects both sender and receiver.
Sender has more information than the rec
Sequential Equilibrium
McGill University
Econ 546
A SSESSMENT
An assessment in an extensive game is a pair consisting of a behavioural strategy
prole and a belief system.
E XAMPLE : R AISE OR M EET
An
Mechanism Design
McGill University
Econ 546
H OW TO B UILD (F UND ) A B RIDGE
Two people in the economy, Eric and Roger.
Should we build the bridge?
How should it be paid for?
Costs 40 to build the br
Bayesian Games
McGill University
Econ 546
G AMES OF I NCOMPLETE I NFORMATION
I Incomplete information: When players do not know (with certainty)
the preferences, payoffs or set of actions of other pla
Extensive Form Games
Subgame Perfection
McGill University
Econ 546
E XTENSIVE F ORM G AMES
I Set of players.
I Set of (decision) nodes. (who moves when)
I For each player and for every node when they
Bayesian Games - II
McGill University
Econ 546
G ENERAL B AYESIAN G AMES
A set of players.
For each player i a set of actions, Si .
For each player i a set of types, i .
For each player i of type i ,
Extensive Form Games
Information Sets
Commitment
McGill University
Econ 546
S IMULTANEOUS M OVES
Up
Down
Left
3, 3
4, 6
Right
6, 4
1, 1
How can we represent this game in extensive form?
I NFORMATION S
Mixed Strategy Equilibrium
McGill University
Econ 546
A N E XAMPLE
U
D
Nash Equilibria?
L
10, 8
5, 4
R
0, 12
7, 2
G ENERAL S TRATEGIC G AMES
Set of players.
For each player, a set of actions and the s
Uncertainty in Extensive Form Games
McGill University
Econ 546
M IXED AND B EHAVIOR S TRATEGIES
A mixed strategy is a probability distribution over strategies in the normal
form.
A behavior strategy s
Discounting and Repeated Games
McGill University
Econ 546
I NTEREST R ATES AND D ISCOUNT FACTORS
Interest at an annual rate r, paid annually.
$1 in the bank earns $1 + r next year.
Discount Factor
To
Repeated Games and the Folk Theorem
McGill University
Econ 546
S OCIAL F EASIBILITY AND I NDIVIDUAL R ATIONALITY
Individual Rationality: Each player gets at least what they can get when
they know the
Strategic Games
McGill University
Econ 546
S TRATEGIC G AMES
Ingredients
I Set of players.
I For each player, a set of actions.
I For each player, preferences over outcomes(action proles).
S TRATEGIC
Nash Equilibrium
McGill University
Econ 546
S HARP P REDICTIONS
a
b
c
d
e
9, 0
6, 0
3, 7
4, 8
f
2, 1
3, 8
5, 3
1, 6
g
5, 3
2, 9
3, 7
1, 4
h
6, 2
1, 4
6, 3
8, 9
Which outcomes survive the iterated elim
Iterated Dominance
McGill University
Econ 546
P REDICTIONS ?
I Strictly dominated strategy There is a different strategy that always does
strictly better, irrespective of what others do.
I Weakly domi
Econ 546A Exam, December 2004 1
McGill University
Faculty of Arts
Final Examination
Game Theory
Econ 546A
Examiner: Prof. LicunXuo Wednesday, Dec. 8, 2004
Associate Examiner: Prof. Hassan Benchekroun