We investigate equilibrium in the buyer's bid double auction (BBDA) in a model with correlated signals and either private or interdependent values. Using a combination of theorems and numerical experiments, we demonstrate that simple equilibria exist even in small markets. Moreover, we bound traders' strategic behavior as a function of market size and derive rates of convergence to zero of (i) inefficiency in the allocation caused by strategic behavior and (ii) the error in the market price as an estimate of the rational expectations price. These rates together with numerical experiments suggest that strategic behavior is inconsequential even in small markets in its effect on allocational efficiency and information aggregation. The BBDA thus simultaneously accomplishes both the informational and allocational goals that markets ideally fulfill; it does this perfectly in large markets and approximately in small markets, with the error attributable mainly to the smallness itself and not the strategic behavior of traders.
Mark Satterthwaite, Steven R. Williams, Konstantinos E. Zachariadis
Satterthwaite, Mark, Steven R. Williams, and Konstantinos E. Zachariadis. 2015. Price Discovery.