Fully Distributed Tâtonnement for Chores Markets

2026-06-30

AI Summary

In trivial markets, traditional price adjustment mechanisms based on excess demand may diverge and struggle to compute competitive equilibria (CE). This work proposes a fully decentralized multiplicative tâtonnement dynamic in which each good independently updates its price solely based on its own excess demand, without requiring global coordination. The mechanism is the first to provably converge to a CE under purely local price updates while implicitly preserving the aggregate price structure. Leveraging Walras’ law and properties of constant elasticity of substitution (CES) and more generally constant curvature homogeneous (CCH) disutility functions, the authors theoretically establish convergence to CE for any CCH disutility function and provide an $O(1/\varepsilon^2)$ rate for approximate convergence in the CES case. Empirical results demonstrate nearly an order-of-magnitude speedup in practical runtime.

Abstract

We study price-adjustment dynamics for computing competitive equilibria (CE) in Fisher markets with chores. Unlike in classical goods markets, prices in chores markets are payments for taking on undesirable tasks, and natural excess-demand dynamics can fail; even the naïve analogue of Walrasian tâtonnement may diverge. Recent work of Chaudhury et al. [2025] overcomes this obstacle via relative tâtonnement, which subtracts the average excess-demand signal from the excess demand vector. This recovers convergence, but at the cost of coupling the price updates across all chores. This leaves open whether such global coupling is inherent, or whether convergent tâtonnement can be recovered through a genuinely local update in which each chore reacts only to its own excess demand. We answer this question affirmatively through multiplicative tâtonnement, a fully distributed dynamics in which each chore price is updated using only its current price and its own excess-demand signal. Although the update contains no explicit normalization term, Walras' law and the multiplicative form of the update implicitly preserve the relevant aggregate price geometry. We prove that multiplicative tâtonnement converges to a CE in any chores Fisher market with continuous, convex, and $1$-homogeneous (CCH) disutilities. For convex CES disutilities, we further prove an approximate-CE convergence rate with the same $O(1/\varepsilon^2)$ dependence as relative tâtonnement, but with improved dependence on problem constants. Experiments on real-world and simulated instances show that multiplicative tâtonnement is substantially faster in practice, often by an order of magnitude.

Problem

• chores markets
• competitive equilibrium
• tâtonnement
• distributed dynamics
• excess demand

Innovation

• multiplicative tâtonnement
• chores markets
• competitive equilibrium
• fully distributed dynamics
• Fisher markets