Almost all works that study market dynamics consider synchronous dynamics.

Computing market equilibria is a problem of both theoretical and applied interest. Much research to date focuses on the case of static Fisher markets with full information on buyers' utility functions and item supplies. Motivated by real-world markets, we consider an online setting: individuals have linear, additive utility functions; items arrive sequentially and must be allocated and priced irrevocably.

This study explores the potential of large language models (LLMs) to conduct market experiments, aiming to understand their capability to comprehend competitive market dynamics. We model the behavior of market agents in a controlled experimental setting, assessing their ability to converge toward competitive equilibria. The results reveal the challenges current LLMs face in replicating the dynamic decision-making processes characteristic of human trading behavior. Unlike humans, LLMs lacked the capacity to achieve market equilibrium. The research demonstrates that while LLMs provide a valuable tool for scalable and reproducible market simulations, their current limitations necessitate further advancements to fully capture the complexities of market behavior. Future work that enhances dynamic learning capabilities and incorporates elements of behavioral economics could improve the effectiveness of LLMs in the economic domain, providing new insights into market dynamics and aiding in the refinement of economic policies.

T\^atonnement is a simple, intuitive market process where prices are iteratively adjusted based on the difference between demand and supply. Many variants under different market assumptions have been studied and shown to converge to a market equilibrium, in some cases at a fast rate. However, the classical case of linear Fisher markets have long eluded the analyses, and it remains unclear whether t\^atonnement converges in this case. We show that, for a sufficiently small step size, the prices given by the t\^atonnement process are guaranteed to converge to equilibrium prices, up to a small approximation radius that depends on the stepsize. To achieve this, we consider the dual Eisenberg-Gale convex program in the price space, view t\^atonnement as subgradient descent on this convex program, and utilize novel last-iterate convergence results for subgradient descent under error bound conditions. In doing so, we show that the convex program satisfies a particular error bound condition, the quadratic growth condition, and that the price sequence generated by t\^atonnement is bounded above and away from zero. We also show that a similar convergence result holds for t\^atonnement in quasi-linear Fisher markets. Numerical experiments are conducted to demonstrate that the theoretical linear convergence aligns with empirical observations.

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.

We study Proportional Response Dynamics (PRD) in linear Fisher markets where participants act asynchronously. We model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. We show that if every bidder individually uses the PRD update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. Our proof technique uncovers further properties of linear Fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.