Large-Scale Contextual Market Equilibrium Computation through Deep Learning

TL;DR

This paper introduces MarketFCNet, a deep learning approach for efficiently approximating large-scale market equilibria with contextual buyers and goods, significantly reducing computation time while maintaining accuracy.

Contribution

The paper presents a novel neural network-based method for large-scale market equilibrium computation that scales efficiently with market size and introduces a new evaluation metric called Nash Gap.

Findings

MarketFCNet achieves competitive accuracy in approximating market equilibrium.

The method significantly reduces computation time compared to traditional algorithms.

Performance improves as market scale increases.

Abstract

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.