Walrasian tatonnement has been a fundamental assumption in economics ever since Walras' general equilibrium theory was introduced in 1874. Nearly a century after its introduction, Vernon Smith relaxed the Walrasian tatonnement assumption by showing that neoclassical competitive market theory explains the equilibrating forces in "double-auction" markets. I make a next step in this evolution by exploring the predictive power of neoclassical theory in decentralized naturally occurring markets. Using data gathered from two distinct markets --the sports card and collector pin markets -- I find a tendency for exchange prices to approach the neoclassical competitive model prediction after a few market periods.