# Large-Scale Contextual Market Equilibrium Computation through Deep Learning

arXiv: https://arxiv.org/abs/2406.15459 · HTML: https://mlsanity.com/paper/2406.15459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 67 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 30 of 30)

- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [A Permutation-Equivariant Neural Network Architecture For Auction Design](https://mlsanity.com/paper/2003.01497/) (2020)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Multiplicative Pacing Equilibria in Auction Markets](https://mlsanity.com/paper/1706.07151/) (2017)
- [Online Nash Social Welfare Maximization with Predictions](https://mlsanity.com/paper/2008.03564/) (2020)
- [Pacing Equilibrium in First-Price Auction Markets](https://mlsanity.com/paper/1811.07166/) (2018)
- [Solving Heterogeneous General Equilibrium Economic Models with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.16977/) (2021)
- [Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers](https://mlsanity.com/paper/2210.09257/) (2022)
- [Online Market Equilibrium with Application to Fair Division](https://mlsanity.com/paper/2103.12936/) (2021)
- [Convex Program Duality, Fisher Markets, and Nash Social Welfare](https://mlsanity.com/paper/1609.06654/) (2016)
- [Contextual Standard Auctions with Budgets: Revenue Equivalence and Efficiency Guarantees](https://mlsanity.com/paper/2102.10476/) (2021)
- [Nonstationary Dual Averaging and Online Fair Allocation](https://mlsanity.com/paper/2202.11614/) (2022)
- [Computing large market equilibria using abstractions](https://mlsanity.com/paper/1901.06230/) (2019)
- [Is Nash Equilibrium Approximator Learnable?](https://mlsanity.com/paper/2108.07472/) (2021)
- [Online Nash Welfare Maximization Without Predictions](https://mlsanity.com/paper/2211.03077/) (2022)
- [Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning](https://mlsanity.com/paper/2303.04833/) (2023)
- [Dynamics of Distributed Updating in Fisher Markets](https://mlsanity.com/paper/1806.04746/) (2018)
- [First-Order Methods for Large-Scale Market Equilibrium Computation](https://mlsanity.com/paper/2006.06747/) (2020)
- [Fisher Markets with Linear Constraints: Equilibrium Properties and Efficient Distributed Algorithms](https://mlsanity.com/paper/2106.10412/) (2021)
- [Enabling First-Order Gradient-Based Learning for Equilibrium Computation in Markets](https://mlsanity.com/paper/2303.09500/) (2023)
- [Learning to Clear the Market](https://mlsanity.com/paper/1906.01184/) (2019)
- [Scalable Fair Division for 'At Most One' Preferences](https://mlsanity.com/paper/1909.10925/) (2019)
- [Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements](https://mlsanity.com/paper/2205.00825/) (2022)
- [Are Equivariant Equilibrium Approximators Beneficial?](https://mlsanity.com/paper/2301.11481/) (2023)
- [Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees](https://mlsanity.com/paper/2308.09277/) (2023)
- [Approximating Equilibrium under Constrained Piecewise Linear Concave Utilities with Applications to Matching Markets](https://mlsanity.com/paper/2107.05700/) (2021)
- [A Framework of Transaction Packaging in High-throughput Blockchains](https://mlsanity.com/paper/2301.10944/) (2023)
- [Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates](https://mlsanity.com/paper/2303.00506/) (2023)

## Abstract (arXiv)

Market equilibrium is one of the most fundamental solution concepts in economics and social optimization analysis. Existing works on market equilibrium computation primarily focus on settings with relatively few buyers. Motivated by this, our paper investigates the computation of market equilibrium in scenarios with a large-scale buyer population, where buyers and goods are represented by their contexts. Building on this realistic and generalized contextual market model, we introduce MarketFCNet, a deep learning-based method for approximating market equilibrium. We start by parameterizing the allocation of each good to each buyer using a neural network, which depends solely on the context of the buyer and the good. Next, we propose an efficient method to unbiasedly estimate the loss function of the training algorithm, enabling us to optimize the network parameters through gradient. To evaluate the approximated solution, we propose a metric called Nash Gap, which quantifies the deviation of the given allocation and price pair from the market equilibrium. Experimental results indicate that MarketFCNet delivers competitive performance and significantly lower running times compared to existing methods as the market scale expands, demonstrating the potential of deep learning-based methods to accelerate the approximation of large-scale contextual market equilibrium.