Before revision:  Using an asymptotic fluid analysis of the two-dimensional Markov process of buyers and sellers, we show that when the matching utility distribution is light-tailed, \% (i.e., the expected value of the maximum of many random variables is a regularly varying function with \alpha=0) the population threshold policy with threshold n{\ln n} is asymptotically optimal among all policies that make matches only at agent arrival epochs.
After revision:  Using a fluid analysis of the two-dimensional Markov process of buyers and sellers, we show that when the matching utility distribution is light-tailed, \% (i.e., the expected value of the maximum of many random variables is a regularly varying function with \alpha=0) the population threshold policy with threshold n{\ln n} is asymptotically optimal among all policies that make matches only at agent arrival epochs.