  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 a relatively small
number of 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 estimate the loss function of the training
algorithm unbiasedly, enabling us to optimize the network parameters through
gradient descent. To evaluate the approximated solution, we introduce 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.
