# Computing large market equilibria using abstractions

arXiv: https://arxiv.org/abs/1901.06230 · HTML: https://mlsanity.com/paper/1901.06230/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2019.

## Built on by (most cited first, 4 of 4)

- [Learning Fair Division from Bandit Feedback](https://mlsanity.com/paper/2311.09068/) (2023)
- [Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games](https://mlsanity.com/paper/2311.00676/) (2023)
- [Solving optimization problems with Blackwell approachability](https://mlsanity.com/paper/2202.12277/) (2022)
- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)

## Abstract (arXiv)

Computing market equilibria is an important practical problem for market design, for example in fair division of items. However, computing equilibria requires large amounts of information (typically the valuation of every buyer for every item) and computing power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share/proportionality when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: (1) filling in unknown valuations using techniques from matrix completion, (2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions.