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

TL;DR

This paper investigates how market connectivity influences the speed and stability of price convergence using a mathematical model, revealing the importance of network structure in market dynamics.

Contribution

It introduces a quantitative analysis linking market structure, specifically algebraic connectivity, to price equilibration and noise tolerance in continuous-time market models.

Findings

Algebraic connectivity determines the rate of price convergence.

Market structure affects the market's resilience to external noise.

The model provides insights into conditions for stable price signaling.

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 t\^{a}tonnement 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.