Title: The Invisible Hand of Laplace
Abstract: I will discuss the role that graph expansion plays in the dynamics of price equilibration in a free market. There is no quantitative explanation in Economics of how markets composed of myopic, self-interested agents, equilibrate; indeed there is no agreement even on the "microscopic" question of how to model the actions, out of equilibrium, of an individual agent. We adopt a simple model of agent actions (Samuelson, 1941) and, in a "toy" Arrow-Debreu market, we show that the convergence rate of the market is determined by the spectrum of an associated Laplacian. Robustness of this prediction follows from stability of Laplacians. I'll also describe why such a "market in isolation" result predicts, for a market not in isolation, the variance of market prices around the equilibrium point. Time permitting, I will describe how work in progress to extend these results to less "toy" markets, relates to questions about matrix perturbations.
Based on joint work with Yuval Rabani (Hebrew U) and on ongoing work.