The Invisible Hand of Dynamic Market Pricing

TL;DR

This paper investigates how dynamic pricing strategies can ensure maximum social welfare in matching markets with sequential buyer arrivals, even without prior knowledge of future buyers, and explores the limits of such approaches.

Contribution

It introduces methods for computing dynamic prices that guarantee social welfare maximization in certain market models without knowing future buyer identities.

Findings

Dynamic prices can maximize social welfare in matching markets.

Such pricing strategies are impossible in general for coverage valuations.

Extensions to Bayesian and bounded rationality models are provided.

Abstract

Walrasian prices, if they exist, have the property that one can assign every buyer some bundle in her demand set, such that the resulting assignment will maximize social welfare. Unfortunately, this assumes carefully breaking ties amongst different bundles in the buyer demand set. Presumably, the shopkeeper cleverly convinces the buyer to break ties in a manner consistent with maximizing social welfare. Lacking such a shopkeeper, if buyers arrive sequentially and simply choose some arbitrary bundle in their demand set, the social welfare may be arbitrarily bad. In the context of matching markets, we show how to compute dynamic prices, based upon the current inventory, that guarantee that social welfare is maximized. Such prices are set without knowing the identity of the next buyer to arrive. We also show that this is impossible in general (e.g., for coverage valuations), but consider other scenarios where this can be done. We further extend our results to Bayesian and bounded rationality models.