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.

翻译：市场均衡是经济学与社会优化分析中最基本的解概念之一。现有关于市场均衡计算的研究主要集中于买方数量相对较少的场景。受此启发，本文研究了大规模买方群体情境下的市场均衡计算问题，其中买方与商品均通过其情境特征进行表征。基于这一现实且广义的情境化市场模型，我们提出了MarketFCNet——一种基于深度学习的市场均衡近似计算方法。我们首先通过神经网络对每个商品分配给每个买方的配置进行参数化，该网络仅依赖于买方与商品的情境特征。随后，我们提出了一种高效的无偏训练算法损失函数估计方法，从而能够通过梯度下降优化网络参数。为评估近似解的质量，我们引入了名为"纳什间隙"的度量指标，用于量化给定配置与价格对相对于市场均衡的偏离程度。实验结果表明，随着市场规模扩大，MarketFCNet在保持竞争力的性能表现的同时，其运行时间显著低于现有方法，这证明了基于深度学习的方法在加速大规模情境化市场均衡近似计算方面的潜力。