动态市场均衡追踪的分布式自适应方法
Tracing Equilibrium in Dynamic Markets via Distributed Adaptation
摘要：
竞争均衡是经济学中的一个核心概念，在市场之外有许多应用，例如调度，商品的公平分配或网络中的带宽分配。竞争均衡的计算在算法博弈论中引起了很大的兴趣，主要是在Fisher市场的突出案例中。自然和分散的过程，如tatonnement和比例响应动态（PRD）收敛迅速向大类费雪市场的均衡。几乎所有的文献都假设市场是一个静态的环境，代理人和商品的参数不随时间而变化。相比之下，许多大型的现实世界市场经常发生动态变化。在本文中，我们提供了第一个可证明的性能保证的离散时间tatonnement和PRD的市场，受到扰动随时间的推移。我们用CES效用分析了Fisher市场的主要类别，并量化了商品供应、代理商预算和代理商效用函数的变化对市场均衡收敛的影响。由于平衡成为一个动态的对象，很少会达到，我们的分析提供了边界表示的距离平衡，将保持通过tatonnement和PRD更新。我们的研究结果表明，在许多情况下，tatonnement和珠三角遵循均衡相当密切，并迅速恢复近似市场出清的条件。我们的方法可以推广到分析一般类的李雅普诺夫动力系统与变化的系统参数，这可能是独立的利益。
英文摘要：
Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest.
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