# Proportional Response Dynamics in Gross Substitutes Markets

arXiv: https://arxiv.org/abs/2506.02852 · HTML: https://mlsanity.com/paper/2506.02852/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications](https://mlsanity.com/paper/2506.03464/) (2025)

## Abstract (arXiv)

Proportional response is a well-established distributed algorithm which has been shown to converge to competitive equilibria in both Fisher and Arrow-Debreu markets, for various sub-families of homogeneous utilities, including linear and constant elasticity of substitution utilities. We propose a natural generalization of proportional response for gross substitutes utilities, and prove that it converges to competitive equilibria in Fisher markets. This is the first convergence result of a proportional response style dynamics in Fisher markets for utilities beyond the homogeneous utilities covered by the Eisenberg-Gale convex program. We show an empirical convergence rate of O(1/T) for the prices. Furthermore, we show that the allocations of a lazy version of the generalized proportional response dynamics converge to competitive equilibria in Arrow-Debreu markets.