Efficiency of Large Double Auctions

MANY MARKET SETTINGS are approximated by a double auction. Standard examples are the London gold market and the order books maintained by New York Stock Exchange specialists. These auctions typically have many traders on each side of the market. More importantly, large double auctions are an excellent model for microfoundations of price formation in competitive markets. Like a competitive market, a large double auction has many traders. However, unlike the standard competitive model, traders are strategic. Hence, if traders asymptotically ignore their effect on price, this is a result, not an assumption, and there is an explicit mechanism translating individual behaviors into prices. So one of the thorniest problems of the standard Walrasian model—how does the market get to equilibrium if everyone is a price taker—is explicitly addressed. Finally, double auctions are a better setting for thinking about price formation than one-sided auctions, both because they are often a better match to reality and, especially, because they capture the essential problems of trade better than a one-sided auction. A large one-sided auction allows one to ask if traded units end up in the right hands, but it does not address whether the correct number of units trade in the first place. In a seminal paper, Rustichini, Satterthwaite, and Williams (1994, henceforth RSW) consider a double auction in which n buyers and sellers draw private values independently and identically distributed. They show that symmetric, increasing, differentiable equilibria in this setting are in the limit efficient and that convergence is fast, of order 1/n2. This is especially attractive in light of experimental evidence on efficiency in double auctions with only a moderate number of players.2