The Sorting Effect of Price Competition

Joint with: Jan Eeckhout

We investigate under which conditions price competition leads to sorting of buyers and sellers. In a decentralized Walrasian market where sellers post prices and buyers choose whom to buy from positive assortative matching obtains only if there is a high enough degree of complementarity between buyer and seller types. 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. Negative assortative matching obtains whenever the match value function is weakly submodular.

For more information, contact Philipp Kircher.