The Invisible Hand of Laplace: the Role of Market Structure in Price Convergence and Oscillation
In a free market, the rise or fall of a price signals excess demand or supply. If the dynamics of price adjustment work well, signaling can enable goods to clear and prices to equilibrate. This is after all the rationale for studying equilibrium theories. fundamental question about a market is therefore 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, and characterize how the algebraic connectivity of the market determines the effectiveness of price signaling equilibration. This also lets us study the level of external noise that a market can tolerate and still maintain near-equilibrium prices. Our work is within a standard model: Arrow-Debreu markets with Samuelson's continuous-time tatonnement dynamics.
Joint work with Yuval Rabani (Hebrew U)