On the Game‐theoretic Foundations of Competitive Search Equilibrium*

Abstract

We provide a unified directed search framework with general production and matching specifications that encompasses most of the existing literature. We prove the existence of subgame perfect Nash equilibria in pure firm strategies in a finite version of the model.We use this result to derive a more complete characterization of the equilibrium set for the finite economy and to extend convergence results as the economy becomes large to general production and matching specifications. The latter extends the micro-foundations for the standard market-utility assumption used in competitive search models with a continuum of agents to new environments.

Market Power and Efficiency in a Search Model*

“…Assume that Condition C1 holds. The characterization results in Galenianos and Kircher (2009b) guarantee that in the unconstrained equilibrium all high productivity firms post and all low productivity firms post .…”

“…Comparing the efficiency requirement () with the equilibrium condition () reveals that efficiency is only achieved when the second ratio of () is equal to one for all pairs of firms. This holds for the case when firms are homogeneous ( x 1 =⋯= x m ) and workers apply to each firm with identical probability (Galenianos and Kircher, 2009b, establish that homogeneous firms post the same wage, and therefore efficiency obtains in that case). However, we will show that when firms are heterogeneous, this ratio is different from one.…”

“…Galenianos and Kircher (2009b) prove the existence of an equilibrium in pure strategies by firms. Furthermore, under an additional condition it is shown that the equilibrium is characterized by the firms’ first‐order conditions and that more productive firms post higher wages and firms with the same productivity post the same wage.…”

“…We replicate the analysis of . The existence and characterization of equilibrium is analyzed in Galenianos and Kircher (2009b), so simply describes the model. The subsequent sections generalize our inefficiency result and examine the effects of policy.…”

“…In the general m ‐firm model, all firms attract applications if their productivity levels are not very far apart. See Galenianos and Kircher (2009b).…”