Do Prices Coordinate Markets?

TL;DR

This paper investigates how well approximate market prices coordinate allocations without coordinated tie-breaking, showing under certain conditions that overdemand remains minimal and prices are robust to market changes.

Contribution

It introduces a genericity condition ensuring minimal overdemand with Matroid Based Valuations and demonstrates the robustness of such prices under market variations.

Findings

Overdemand is at most 1 under certain conditions, regardless of supply.

Prices are robust to changes in buyers if they are sampled from the same distribution.

The results hold even with uncoordinated tie-breaking and approximate equilibrium prices.

Abstract

Walrasian equilibrium prices can be said to coordinate markets: They support a welfare optimal allocation in which each buyer is buying bundle of goods that is individually most preferred. However, this clean story has two caveats. First, the prices alone are not sufficient to coordinate the market, and buyers may need to select among their most preferred bundles in a coordinated way to find a feasible allocation. Second, we don't in practice expect to encounter exact equilibrium prices tailored to the market, but instead only approximate prices, somehow encoding "distributional" information about the market. How well do prices work to coordinate markets when tie-breaking is not coordinated, and they encode only distributional information? We answer this question. First, we provide a genericity condition such that for buyers with Matroid Based Valuations, overdemand with respect to equilibrium prices is at most 1, independent of the supply of goods, even when tie-breaking is done in an uncoordinated fashion. Second, we provide learning-theoretic results that show that such prices are robust to changing the buyers in the market, so long as all buyers are sampled from the same (unknown) distribution.