Private Knowledge vs. Common Knowledge Carlson and Van Dam (see Econometrica, 1991) and Morris and Shin (see AER, 1998)

Coordination Game 0,24,4 3,32,0 A B A B Two Equilibria: (4,4) and (3,3)

Carlson-Van Dam’s “Global Game” 0+X, 24+X, 4+X 3, 32, 0+X A B A B Add X to Action A And view X as a variable

X -2 3 BB dominates AA dominates Both, AA and BB are Equilibria Global Game:

“Connecting” games together Private Signal Random variable

-2 3 B dominates A dominates Both AA and BB are an Equilibrium 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

-2 3 B dominates A dominates X*=1/2 Cutoff X is determined so that player is indifferent between playing A or playing B: A-RD B-RD A-PD At X=0, (the original game), BB or AA with 50-50=risk dominance PD=Pereto dominance RD=Risk dominance

Morris and Shin Random fundamental Floating Exchange rate Pegged exchange rate Speculators’ cost of attack: t>0 Speculator’s gain if peg abandoned:

Speculators’ cost of attack: t>0 Speculator’s gain if peg abandoned: Government value of defending peg: Gov’t cost of defending: Gov’t observes: Government indifference: Government defends if: - fraction of attackers in the population C() increases in alpha decreases in theta

Dominance region for attack speculators (abandons peg below even if no one Attacks.) Attack strategy dominates

(no attack above even if government abandons peg.) Attack strategy dominates No-attack strategy dominates Potential Multiple Equilibria

Signals Sequence of steps: 1. Realized; 2. Speculators observe-- small 3. Government observes and decides on peg-- Abandons if

Attack strategy dominates No-attack strategy dominates Potential Multiple equilibria

Probability that government abandons the peg An indifference at : t=prob.gain=