Supplementary Appendix to “Incentive Compatibility of Large Centralized Matching Markets”

First, we summarize definitions and related theorems of asymptotic statistics in Section A. We prove Theorems in Section B. Lastly, Section C contains additional simulation results. A Asymptotic Statistics We summarize some results of asymptotic statistics from (Serfling, 1980). Let X1, X2, . . . and X be random variables on a probability space (Ω,A, P ). We say that Xn converges in probability to X if lim n→∞ P (|Xn −X| < ) = 1, every > 0. This is written Xn p −→ X. For r > 0, we say that Xn converges in the r th mean (or in the L-norm) to X if lim n→∞ E (|Xn −X|) = 0. This is written Xn Lr −→ X. Fact 1. If Xn Lr −→ X, then Xn p −→ X. ∗Department of Economics, University of Pennsylvania. E-mail: sangmok-at-sas.upenn.edu