Analyzing Tatonnement Dynamics in Economic Markets

详细信息   

• 作者：Cheung ; Yun Kuen
• 学历：Doctor
• 年：2014
• 关键词：Social sciences ; Applied sciences ; Gradient descent
• 导师：Cole,Richard J.
• 毕业院校：New York University
• Department：Computer Science
• 专业：Economic theory;Computer science
• ISBN：9781321374193
• CBH：3665116
• Country：USA
• 语种：English
• FileSize：1995613
• Pages：183

文摘

The impetus for this dissertation is to explain why well-functioning markets might be able to stay at or near a market equilibrium. We argue that tatonnement,a natural,simple and distributed price update dynamic in economic markets,is a plausible candidate to explain how markets might reach their equilibria. Tatonnement is broadly defined as follows: if the demand for a good is more than the supply,increase the price of the good,and conversely,decrease the price when the demand is less than the supply. Prior works show that tatonnement converges to market equilibrium in some markets while it fails to converge in other markets. Our goal is to extend the classes of markets in which tatonnement is shown to converge. The prior positive results largely concerned markets with substitute goods. We seek market constraints which enable tatonnement to converge in markets with complementary goods,or with a mixture of substitutes and complementary goods. We also show fast convergence rates for some of these markets. This dissertation is divided into two parts: * In Part I,we will focus on properties of the aggregate demand rather than properties of individual buyers' demands. We show that when demand and income elasticities are suitably bounded,tatonnement converges quickly in certain markets with complementary goods. We also introduce a new type of elasticity,adverse market elasticity,and show that tatonnement converges quickly in markets with a mixture of substitutes and complements,when this elasticity is suitably bounded. To have a realistic market setting for a price adjustment mechanism,out-of- equilibrium trade must be allowed so as to generate demand imbalances that then induce price adjustments. The ongoing market model is a fairly new market model which enables out-of-equilibrium trade,and also captures the distributed nature of markets by allowing independent and asynchronous price updates. Our analysis in Part I handles both the classical market setting and the ongoing market setting. We introduce an amortized analysis technique to handle asynchronous events--in our case asynchronous price updates. We devise a potential function that decreases substantially and continuously when there is no price update,and in addition the potential function does not increase upon a price update. This amortized analysis technique may be of independent interest. * In Part II,we define a new class of markets called Convex Potential Function Markets (CPF markets),in which tatonnement is equivalent to gradient descent. The equivalence opens up the entire toolbox developed to analyse gradient descent and provides a principled approach to show convergence of the tatonnement process. We show that Eisenberg-Gale markets,a fairly new class of markets,are contained in CPF markets. This allows us to prove that tatonnement converges in many interesting classes of markets,including Fisher markets with Leontief,complementary-CES or nested-CES utility functions. For Fisher markets with Leontief or complementary-CES utilities,we bound the convergence rates,either by established tools for analysing gradient descent,or by showing that the potential function demonstrates strong sandwiching property,a new property we introduce that enables us to show rapid convergence. This property may be of independent interest.