The WALRAS Algorithm : A Convergent Distributed Implementation of GeneralEquilibrium

The walras algorithm calculates competitive equilibria via a distributed tatonnement-like process, in which agents submit single-good demand functions to market-clearing auctions. The algorithm is asynchronous and decentralized with respect to both agents and markets, making it suitable for distributed implementation. We present a formal description of this algorithm, and prove that it converges under the standard assumption of gross substitutability. We relate our results to the literature on general equilibrium stability and some more recent work on decentralized algorithms. We present some experimental results as well, particularly for cases where the assumptions required to guarantee convergence do not hold. Finally, we consider some extensions and generalizations to the walras algorithm. 1. Distributed Implementation of General Equilibria 1.1. Tatonnement When a collection of interconnected markets achieves a perfect balance of supply and demand with respect to the maximizing behaviors of self-interested economic agents, we say that the economy is in general equilibrium. This idea of a general price equilibrium was originally articulated by L eon Walras (1874), who proposed that such equilibria could be realized through a price-adjustment process he called tatonnement (sometimes translated as \groping", or \tentative proceedings"), in which agents (that is, consumers and producers) respond to price signals for the individual goods. The agents' interactions are coordinated by a central \auction-eer" who adjusts the general price levels toward a general balance, announcing interim prices to elicit responses from the agents. More speciically, Walras envisioned the market clearing process working as follows. 1 Starting with a set of prices arbitrarily given, the excess demand in each market may be positive, zero, or negative. For an arbitrary ordering of these markets , take the rst and adjust the price so that supply and demand are equal, given all other prices. Of course, the change in the rst price will normally change Department of Economics. 1 See Lesson 12 of the original source (Walras 1874), or, for a more accessible exposition, Arrow and Hahn's account (1971, Chapter 1).