Do Prices Coordinate Markets?
Justin Hsu, Jamie Morgenstern, Ryan Rogers, Aaron Roth, Rakesh Vohra

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…
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