Strategic Complementarities and Search Market Equilibrium

Abstract

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for strategic complementarities and prove existence of search market equilibrium. When firms are identical, the Diamond Paradox obtains and is robust within the class of search cost densities that are small near zero and support strategic complementarities. Price dispersion is therefore inherently incompatible with strategic complementarities. Finally, we show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.

Keywords: Diamond Paradox, price dispersion, search, strategic complementarities

JEL Classification: D43, D83