Online Appendix to: Socially-Optimal Design of Service Exchange Platforms with Imperfect Monitoring

A. PROOF OF PROPOSITION 4.1 A.1. The Claim to Prove In order to prove Proposition 4.1, we quantify the performance loss of strategies restricted to Aas. The performance loss is determined in the following claim. Claim. Starting from any initial rating profile θ , the maximum social welfare achievable at the PAE by (π0, π · 1N) ∈ (Aas) × N(Aas) is at most b− c − c · ρ(θ , α∗ 0, S∗ B) ∑ s′∈S∗ B q(s′|θ, α∗ 0, αa · 1N), (29)