Online Appendix for Signaling in a Global Game: Coordination and Policy Traps

Lemma 2. For any r∗ ∈ (r, r̃) and ε > 0, there exist η̄ > 0 and ρ̄ < r/r∗ such that for any (η, ρ) < (η̄, ρ̄), conditions (3)-(2) below admit a solution (x0, x̂, θ0, θ00) that satisfies θ0 ≤ θ00, |x0 − x∗| < ε, ̄̄θ0 − θ∗ ̄̄ < ε, ̄̄θ00 − θ∗∗ ̄̄ < ε, and x̂ < −1/ε. 1−Ψ(x−θ σ ) = r − (r − ρr∗)[Ψ(x 0−θ0 σ )−Ψ(x 0−θ00 σ )] (1) 1−Ψ( x̂−θ0 σ ) = r + [r∗ρ+ r∗(1− ρ) exp( r ∗−r η )− r][Ψ( x̂−θ 0 σ )−Ψ( x̂−θ 00 σ )] (2) θ0 = ρ[1− exp(−r−r η )]Ψ( 0−θ0 σ ) + [1− ρ+ ρ exp(− ∗−r η )]Ψ( x̂−θ0 σ ) + C (r ∗) (3) C (r∗) = (1− ρ)[1− exp(− r∗−r η )][Ψ( 0−θ00 σ )−Ψ( x̂−θ 00 σ )] (4) C(r∗) ≤ (1− ρ)[1− exp(−r−r η )][Ψ( 0−θ0 σ )−Ψ( x̂−θ 0 σ )] (5)