Amortized Analysis of Asynchronous Price Dynamics

TL;DR

This paper extends a framework for asynchronous coordinate descent algorithms to analyze asynchronous tatonnement, demonstrating convergence to market equilibrium in Fisher markets with CES or Leontief utilities.

Contribution

It introduces an asynchronous analysis of tatonnement, showing convergence in specific market models, which was not previously established.

Findings

Asynchronous tatonnement converges in Fisher markets with CES utilities.

Asynchronous tatonnement converges in Fisher markets with Leontief utilities.

The framework extends to analyze asynchronous price dynamics in general equilibrium models.

Abstract

We extend a recently developed framework for analyzing asynchronous coordinate descent algorithms to show that an asynchronous version of tatonnement, a fundamental price dynamic widely studied in general equilibrium theory, converges toward a market equilibrium for Fisher markets with CES utilities or Leontief utilities, for which tatonnement is equivalent to coordinate descent.