On the game-theoretic foundations of competitive search equilibrium

We provide a unified directed search framework with general production and matching specifications that encompass 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 microfoundations for the standard market utility assumption used in competitive search models with a continuum of agents to new environments.