Large-Scale Contextual Market Equilibrium Computation through Deep Learning

2024-06-11

arXiv.org

AI Summary

This paper addresses the computational challenge of computing context-aware (buyer/item feature-dependent) market equilibria in large-scale buyer populations. We propose MarketFCNet, the first end-to-end deep learning framework for this task. Methodologically, we formulate equilibrium computation as a differentiable allocation optimization problem, incorporating context-parameterized utility functions and explicit budget constraints. To ensure training stability and solution quality, we design an unbiased loss estimator and a Nash Gap-based evaluation metric. Experiments demonstrate that MarketFCNet achieves up to 100× speedup over traditional numerical solvers on markets with ten thousand buyers, while matching their equilibrium accuracy. Our core contributions are threefold: (i) the first systematic integration of deep learning into context-aware market equilibrium computation; (ii) a theoretically grounded, unbiased training objective and a practical, interpretable evaluation metric; and (iii) empirical validation that neural networks can efficiently approximate complex economic mechanisms with high fidelity.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Computing market equilibrium for large-scale buyer populations
• Developing deep learning method for contextual market models
• Evaluating solution quality with Nash Gap metric

Innovation

• Deep learning-based MarketFCNet for equilibrium
• Neural network parameterizes buyer-good allocation
• Nash Gap metric evaluates solution deviation