The Invisible Hand of Laplace: the Role of Market Structure in Price Convergence and Oscillation

Abstract

A fundamental question about a market is under what conditions, and then how rapidly, does price signaling cause price equilibration. Qualitatively, this ought to depend on how well-connected the market is. We address this question quantitatively for a certain class of Arrow-Debreu markets with continuous-time proportional tâtonnement dynamics. We show that the algebraic connectivity of the market determines the effectiveness of price signaling equilibration. This also lets us study the rate of external noise that a market can tolerate and still maintain near-equilibrium prices.