The complexity of exchange

The computational complexity of two classes of market mechanisms is compared. First the Walrasian interpretation in which prices are centrally computed by an auctioneer. Recent results on the computational complexity are reviewed. The non-polynomial complexity of these algorithms makes Walrasian general equilibrium an implausible conception. Second, a decentralised picture of market processes is described, involving concurrent exchange within transient coalitions of agents. These processes feature price dispersion, yield allocations that are not in the core, modify the distribution of wealth, are always stable, but path-dependent. Replacing the Walrasian framing of markets requires substantial revision of conventional wisdom concerning markets.