Competitive Market Institutions: Double Auctions vs. Sealed Bid-Offer Auctions

Consider a market with the following characteristics: 1) privacy, that is, each agent knows only his own valuation (or cost) conditions; 2) exchange follows the rules of the oral double auction, that is, buyers freely announce bids or accept offers and sellers freely announce offers or accept bids; 3) aggregate market supply and demand per trading period is stationary for at least two to three periods; and 4) there are at least four buyers, and as many sellers. The literature reporting the results of a large number of experimental markets with these characteristics documents what appears to be a remarkably rapid convergence to a competitive equilibrium (CE).' However, any claim of double auction (DA) "convergence" to the CE can only have meaning in one of three senses: (i) The CE is attained immediately. (ii) After T periods of trading, some measure of the market's state, such as mean price, is nearer, relative to experimental sampling variability, to a CE than to some distinct alternative equilibrium such as a monopoly or Nash equilibrium. (iii) After T periods of trading, this measure is nearer to a CE in DA experimental markets than in markets organized under a different institution of contract, for example, a sealed-bid auction. Since everything from electrons and the stars to rats and people yield state measures subject to "error" or random variation, the deterministic criterion (i) can have no serious scientific standing. By such criteria any hypothesis can be rejected and there could be no science of physics, biology, or economics.2 With the exception of certain very simple markets such as single object auctions, or certain idealized markets such as the Cournot quantity adjuster model, economics has only two concepts of equilibrium-monopoly and competitive. The only formal model of DA trading that has been proposed (see David Easley and John Ledyard, p. 6) predicts stochastic convergence (in finite time, with probability one) to a CE. Hence, the only test alternative to the CE research hypothesis in DA markets is a monopoly (or monopsony) equilibrium. Experimentalists have not reported statistical tests of the CE *Professor, department of economics, University of Arizona; assistant professor, department of economics, Indiana University; instructor, department of economics, University of Arizona; and Sandia National Laboratories, Albuquerque, NM, respectively. We are indebted to the National Science Foundation for research support, and to Art Denzau and Mort Kamien for helpful comments. 'There is an early and recently growing body of experimental evidence for convergence to a competitive equilibrium under double auction rules: the earliest evidence (contained in experiments initiated in January 1956) is reported in Smith (1962, 1964, 1965, 1976). However, these early experiments used between twenty and fifty or so participant buyers and sellers because, in keeping with prevailing professional beliefs, it was thought that a CE was unlikely to be approached unless numbers were quite large. Using large numbers was not unreasonable since it is a good beginning procedure to give a theory whatever is believed to be its "best shot." More recent evidence using six buyers, six sellers, and two traders in "speculative" DA markets with cyclical demand is reported by R. M. Miller, Charles Plott, and Smith, and Williams (1979). For evidence from a comparison of oral and computerized DA experiments with four buyers and four sellers, see Williams (1980). For further evidence in the context of the study of price controls, see M. Isaac and Plott (1981b) and Smith and Williams (1981b); in the context of a conspiracy study see Isaac and Plott (1981a); in the context of comparisons between DA and posted offer pricing, see Jon Ketcham, Smith, and Williams; in the context of a study of four variations on DA rules, see Smith and Williams (1980). All of these more recent papers report double auction experiments using no more than four buyers and four sellers. 2As Frederick Mosteller once noted, if you wanted to reject the inverse square law of attraction, try tossing a sheet of paper out the window.