Efficient Repeated Implementation: Supplementary Material

Claim A.2. Fix any σ ∈ Ω(R̂). Also, assume that, for each i, outcome ã ∈ A used in the construction of S above satisfies condition (7) in LS. Then, for any t and θ(t), if g = ĝ then m θ(t),θt i = (·, 0) and m θ(t),θt j = (·, 0) for any θ. Proof. Suppose not; then, for some t, θ(t) and θ, g = ĝ and the continuation regime next period at h(θ(t), θ) is either D or S for some i. By similar reasoning to the ∗Department of Economics, Seoul National University, Seoul 151-746, Korea, [email protected] †Faculty of Economics, Cambridge, CB3 9DD, United Kingdom, [email protected]