Title : Analyzing Tatonnement Dynamics in Economic Markets
Candidate: Yun Kuen Cheung
Advisor: Richard Cole
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.
We introduce an amortized analysis technique to handle asynchronous events - in our case asynchronous price updates. On the other hand, for some markets we show that tatonnement is equivalent to generalized gradient descent (GGD). The amortized analysis and our analysis on GGD may be of independent interests.