Walrasian auction

A Walrasian auction, introduced by Leon 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 suggests that equilibrium will be achieved through a process of "tâtonnement" or "groping".

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 tâtonnement process works as follows: Prices are cried, and agents register how much of each good they would like to offer (supply) or purchase (demand). No transactions and no production take place at disequilibrium prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are raised for goods with excess demand. The question for the economist is under what conditions such a process will terminate in equilibrium in which demand equates to supply for goods with positive prices and demand does not exceed supply for goods with a price of zero. Although Walras was not able to provide a definitive answer to this question subsequent researchers, such as Arrow and Debreu, have provided proofs of existence under some conditions (of which the strongest one is the convexity of preferences). However, the Sonnenschein-Mantel-Debreu Theorem states that an equilibrium need not be unique.

A recent article by Richter and Wong contests the Arrow-Debreu proof and claims the following holds with respect to the computation of Walrasian equilibria:

* The Arrow-Debreu conditions are "not sufficient" to guarantee existence of a computable equilibrium.
* The "rate of approximation" towards an equilibrium (as defined by the current price set) cannot be given under any algorithm.

Selected publications

*cite journal | author=Richter, M.K. & Wong, K-Ch. | title = Non-computability of competitive equilibrium | journal= Economic Theory | year=1999 | volume=14 | pages=1–27 | doi = 10.1007/s001990050281

ee also

* Leon Walras
* Walras' law