On the Foundations of Competitive Search Equilibrium with and Without Market Makers

Working Paper: CEPR ID: DP16342

Authors: James Albrecht; Xiaoming Cai; Pieter A. Gautier; Susan Vroman

Abstract: The literature offers two foundations for competitive search equilibrium, a Nash approach and a market-maker approach. When each buyer visits only one seller (or each worker makes only one job application), the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. Our paper analyzes competitive search equilibrium with simultaneous search using the two approaches. We consider four cases defined by (i) the surplus structure (are the goods substitutes or complements?) and (ii) the mechanism space (do sellers post fees or prices?). With fees, the two approaches yield the same constrained efficient equilibrium. With prices, the equilibrium allocation is the same using both approaches if the goods are complements, but is not constrained efficient. In the case in which only prices are posted and the goods are substitutes, the equilibrium allocations from the two approaches are different.

Keywords: multiple applications; competitive search; market makers; efficiency

JEL Codes: C78; D44; D83

Causal Claims

Cause	Effect
Nash equilibrium may not be constrained efficient (C72)	Nash equilibrium is not constrained efficient when goods are substitutes (C72)
market-maker equilibrium can achieve constrained efficiency (D53)	market-maker equilibrium can achieve constrained efficiency under certain conditions (D53)
equilibrium allocation is the same under both approaches (D51)	equilibrium allocation is the same under both approaches if the goods are complements (D10)
equilibrium allocation diverges (D51)	equilibrium allocation diverges when the goods are substitutes (D51)
efficiency of equilibrium allocation is contingent on mechanism employed (D61)	efficiency of equilibrium allocation is contingent on mechanism employed (fees versus prices) (D61)