Article,
The Sorting Effect of Price Competition
(May 2007)
Abstract
In order to reveal information about buyer valuations, price competition leads to sorting of buyers and sellers. In a decentralized Walrasian market with private values, we show that there is perfect sorting of high valuation buyers with high cost sellers. Such negative assortative matching arises generally in the absence of complementarity. Positive assortative matching obtains only if there is a high enough degree of complementarity. The relevant condition is root-supermodularity; i.e., the square root of the match value function is supermodular. This condition is weaker than log-supermodularity, a condition required for positive assortative matching in markets with random search.
