# Walrasian Dynamics in Multi-unit Markets

arXiv: https://arxiv.org/abs/1712.08910 · HTML: https://mlsanity.com/paper/1712.08910/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2017.

## Built on by (most cited first, 2 of 2)

- [Learning and Collusion in Multi-unit Auctions](https://mlsanity.com/paper/2305.17402/) (2023)
- [AI-driven Prices for Externalities and Sustainability in Production Markets](https://mlsanity.com/paper/2106.06060/) (2021)

## Abstract (arXiv)

In a multi-unit market, a seller brings multiple units of a good and tries to sell them to a set of buyers that have monetary endowments. While a Walrasian equilibrium does not always exist in this model, natural relaxations of the concept that retain its desirable fairness properties do exist. We study the dynamics of (Walrasian) envy-free pricing mechanisms in this environment, showing that for any such pricing mechanism, the best response dynamic starting from truth-telling converges to a pure Nash equilibrium with small loss in revenue and welfare. Moreover, we generalize these bounds to capture all the Nash equilibria for a large class of (monotone) pricing mechanisms. We also identify a natural mechanism, which selects the minimum Walrasian envy-free price, in which for n=2 buyers the best response dynamic converges from any starting profile, and for which we conjecture convergence for any number of buyers.