In order to construct a theory of general equilibrium without an auctioneer we extend models of "search market equilibrium" to incorporate general equilibrium considerations. The model we treat is one with a single product market and a single labor market. Imperfectly informed individuals follow optimal sequential strategies in searching for a suitably low price and high wage. For any distribution of price and wage offers across firms, these optimal strategies generate product demand and labor supply schedules. Firms then choose prices and wages to maximize expected profits, taking these schedules as given, and the resulting profits are paid out to individuals as dividends.
An equilibrium distribution of prices and wages is one which results from optimal price and wage setting behavior by firms given individuals' optimal search strategies. There are two possible equilibrium configurations, a degenerate equilibrium in which all firms charge the same price and wage, and a price and wage dispersion equilibrium. We prove the existence of a degenerate equilibrium and of a price and wage dispersion equilibrium.