Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Columbia University, University of Illinois Urbana-Champaign
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
Awards: G1250462331, CAREER: Fair and Efficient Market Design at Scale, AF:RI:Small: Fairness in allocation and machine learning problems: algorithms and solution concepts, FAI: AI Algorithms for Fair Auctions, Pricing, and Marketing, G4321895214, G4720003262, G6671297155, G8876996369, CAREER: New Frontiers of Fairness in Allocation and Exchange Problems
OpenAlex ID: W7167070442