Tatonnement in ongoing markets of complementary goods

Abstract

This paper continues the study, initiated by Cole and Fleischer in [6], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities.The current work shows that fast convergence also occurs for the following types of markets:• All pairs of goods are complements to each other, and• the demand and income elasticities are suitably bounded.In particular, these conditions hold when all buyers in the market are equipped with CES utilities, where all the parameters ρ, one per buyer, satisfy −1 < ρ ≤ 0.In addition, we extend the above result to markets in which a mixture of complements and substitutes occur. This includes characterizing a class of nested CES utilities for which fast convergence holds.An interesting technical contribution, which may be of independent interest, is an amortized analysis for handling asynchronous events in settings in which there are a mix of continuous changes and discrete events.

Proportional Dynamics in Exchange Economies

“…(See also Fleischer, Garg, Kapoor, Khandekar, and Saberi [39].) This was followed up by similar analysis for some markets with complementarities (Cheung, Cole, and Rastogi [17]; Cheung and Cole [15]; Avigdor, Rabani, and Yadgar [3]), then for all "Eisenberg-Gale" markets in the Fisher model [16]. Some of these analyses apply to ongoing and/or asynchronous settings.…”

The invisible hand of Laplace: The role of market structure in price convergence and oscillation

“…Markets and algorithms. Recent work in computer science [17,24,18,10,15,14,8] [45] were able to show that one of these inequalities breaks down badly. However, the counterexamples are rather delicate, and it is conceivable that reasonable assumptions in the market setting (e.g., bounds on asymmetry in trade) would restore the inequalities (perhaps weakened) and enable application of spectral methods.…”

Convergence of incentive-driven dynamics in Fisher markets

“…However, the classical view of tâtonnement posits the existence of an imaginary "auctioneer" who controls the process by announcing prices. Recent work on the convergence of discretetime tâtonnement in Fisher markets attempts to present it as an in-market process in the context of the so-called ongoing markets [CF08,CCR12]. However, even this attempt requires a somewhat careful choice of the magnitude of the price adjustment which is not motivated by any agent considerations (aside from a common inexplicable passion to equilibrate the economy).…”