New algorithm speeds up chores market equilibrium by 10x

A team of computer science researchers has cracked a long-standing problem in market design with a new algorithm called 'multiplicative tâtonnement' that accelerates equilibrium computation in chores markets by an order of magnitude.

The work, led by Bhaskar Ray Chaudhury, Christian Kroer, Ruta Mehta, and Tianlong Nan, tackles a fundamental challenge in Fisher markets where 'chores' (undesirable tasks) require compensation rather than traditional goods that provide utility. While classical price-adjustment dynamics (tâtonnement) works for goods markets, natural adaptations fail for chores markets due to divergent price updates. The new algorithm achieves full distribution by updating each chore's price using only its own excess-demand signal, eliminating the need for global coordination that plagued previous approaches like relative tâtonnement.

The researchers prove theoretical convergence to competitive equilibria (CE) for continuous, convex, and 1-homogeneous disutilities, with experiments showing dramatic speed improvements—often 10x faster than prior methods—on real-world and simulated datasets. For convex CES disutilities, they achieve O(1/ε²) convergence rates with improved constant dependencies, maintaining the same theoretical guarantees while delivering practical efficiency gains that could transform applications in resource allocation and task assignment systems.