A Walrasian auction, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand.
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.
As a mistranslation
Until Walker and van Daal's 2014 translation, William Jaffé's Elements of Pure Economics (1954) was for many years the only English translation of Walras's Éléments d’économie politique pure.
Walker and van Daal argue that the idea of the Walrasian auction and Walrasian auctioneer resulted from Jaffé's mistranslation of the French word crieurs (criers) into auctioneers. Walker and van Daal call this "a momentous error that has mislead generations of readers into thinking that the markets in Walras's model are auction markets and that he assigned the function of changing prices in his model to an auctioneer."