How Well Do Prices Coordinate Markets
summary
Price vectors are tested as coordinators: minimal Walrasian prices can leave many buyers indifferent, so a genericity condition (valuations linearly independent over integers) is assumed. For unit-demand (and matroid-based/gross-substitute) valuations the claim is concrete: with exact minimal prices the over-demand at most one per good, so excess demand vanishes as supply grows. Using learning tools (compression bounds, pseudo-dimension) prices learned from a sample generalize if supply/samples scale like k/ε^2, giving demand within (1±ε) and similar welfare.
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