Walrasian auction

Walras suggested that equilibrium would always be achieved through a process of tâtonnement (French for "trial and error"), a form of hill climbing. In the 1970s, however, the Sonnenschein–Mantel–Debreu theorem proved that such a process would not necessarily reach a unique and stable equilibrium, even if the market is populated with perfectly rational agents.

Walrasian auctioneer

The Walrasian auctioneer is the presumed auctioneer that matches supply and demand in a market of perfect competition. The auctioneer provides for the features of perfect competition: perfect information and no transaction costs. The process is called tâtonnement, or groping, relating to finding the market clearing price for all commodities and giving rise to general equilibrium.

The device is an attempt to avoid one of deepest conceptual problems of perfect competition, which may, essentially, be defined by the stipulation that no agent can affect prices. But if no one can affect prices no one can change them, so prices cannot change. However, involving as it does an artificial solution, the device is less than entirely satisfactory.