Private Knowledge vs' Common Knowledge

1
Private Knowledge vs. Common Knowledge

• Carlson and Van Dam (Econometrica , 1991) and
  Morris and Shin (AER, 1998)

2
Coordination Game
B
A
A
B
Two equilibria (4,4) and (3,3)
3
Carlson-Van Dams Global Game
B
A
A
B
Add X to Action A And view X as a variable
4
Global Game
X
BB dominates
Both, AA and BB are equilibria
AA dominates
-2
3
5
Connecting games together
Signal
random
6
If my signal is 2 I suspect that the other
player signal is 2 with 50 probability thus
action B dominates
If my signal is 3 I suspect that the other
player signal is 3 with 50 probability thus
action A dominates
B dominates
Both AA and BB are equilibria
A dominates
-2
3
At Xo (original game)BB or AA with 50-50risk
dominance
PDPereto dominance
V(1/2)4(1/2)321/2
RDRisk dominance
7
Cutoff X is determined so that player
is indifferent between playing A or playing B
X1/2
B dominates
A-PD
A dominates
B-RD
A-RD
-2
3
X1/2

8
Morris and Shin
Random fundamental
Floating Exchange rate
Pegged exchange rate
Speculators cost of attack tgt0
Speculators gain if peg abandoned
9
Speculators cost of attack tgt0

Speculators gain if peg abandoned
- fraction of attackers in the population
Government value of defending peg
Govt cost of defending
Govt observes
Govt indifference
Government defends if
C() increases in alpha decreases in theta
10
Dominance region for attack speculators
(abandons peg below even if no one Attacks.)
Attack strategy dominates
11
(no attack above even if government abandons
peg.)
Attack strategy dominates
Potential Multiple equilibria
No-attack strategy dominates
12
Signals
Sequence of steps 1. Realized
2. Speculators observe--
small
3. Government observes and decides
on peg--
Abandons if
13
Attack strategy dominates
Potential Multiple equilibria
No-attack strategy dominates
14
Probability that government abandons the peg

An indifference at
tprob.gain