Approximating welfare in large efficient markets

TL;DR

This paper analyzes large markets with many buyers and sellers, showing that equilibrium trade quantities and welfare are approximately normally distributed, and provides bounds on the approximation accuracy using Gaussian process techniques.

Contribution

It introduces a novel asymptotic normal approximation for welfare and trade quantities in large markets, with explicit bounds on the approximation rate.

Findings

Joint distribution of welfare and trade is asymptotically normal.

Approximation rate bounds are established.

Method applies to various mechanism design problems.

Abstract

We consider the efficient outcome of a canonical economic market model involving buyers and sellers with independent and identically distributed random valuations and costs, respectively. When the number of buyers and sellers is large, we show that the joint distribution of the equilibrium quantity traded and welfare is asymptotically normal. Moreover, we bound the approximation rate. The proof proceeds by constructing, on a common probability space, a representation consisting of two independent empirical quantile processes, which in large markets can be approximated by independent Brownian bridges. The distribution of interest can then be approximated by that of a functional of a Gaussian process. This methodology applies to a variety of mechanism design problems.