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 rms
B ASIC C OMPONENTS
Multiple players
Surplus
The valu
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 receiver about the outcome of the
latters choice.
Asymmetr
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
Anns behavioural strategy as depicted above is Ann (B)(Se
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 bridge.
Eric and Roger are both one of two types(value fo
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 players (and in some
cases their own).
I Different from im
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 move, a set of actions.
I Information sets. What do pla
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 , preference across all outcomes for a given
type prole,
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 ETS
The dotted line represents an information set.
Bob
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 set of all probability distributions
over the set of act
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 species a (conditional) probability distribution over
ac
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 have $1 in the bank tomorrow how much money do you need
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 other players strategy.
Social Feasibility: There is so
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 G AMES
Ingredients
I Set of players.
I For each player,
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 elimination of strictly dominated
strategies?
N ASH E QUILI
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 dominated strategy There is a different strategy that never
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 they move, a set of
actions.
A behavioural strategy is a c