Walrasian auction

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.

Walras suggested that equilibrium would always be achieved through a process of tâtonnement (French for "trial and error"), a form of hill climbing.^[1] 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.^[2]

^ Wurman 1999, p. 87.
^ Ackerman 2002, pp. 122–123, "In Walrasian general equilibrium, prices are adjusted through a tâtonnement ('groping') process: the rate of change for any commodity’s price is proportional to the excess demand for the commodity, and no trades take place until equilibrium prices have been reached. This may not be realistic, but it is mathematically tractable: it makes price movements for each commodity depend only on information about that commodity. Unfortunately, as the SMD theorem shows, tâtonnement does not reliably lead to convergence to equilibrium."

[FOOTNOTEWurman199987-1] Wurman 1999, p. 87.

[FOOTNOTEAckerman2002122–123-2] Ackerman 2002, pp. 122–123, "In Walrasian general equilibrium, prices are adjusted through a tâtonnement ('groping') process: the rate of change for any commodity’s price is proportional to the excess demand for the commodity, and no trades take place until equilibrium prices have been reached. This may not be realistic, but it is mathematically tractable: it makes price movements for each commodity depend only on information about that commodity. Unfortunately, as the SMD theorem shows, tâtonnement does not reliably lead to convergence to equilibrium."

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