Buy-Many Mechanisms for Many Unit-Demand Buyers
Shuchi Chawla, Rojin Rezvan, Yifeng Teng, Christos Tzamos

TL;DR
This paper extends buy-many constraints to multi-buyer settings, proposing a simple pricing mechanism that achieves near-optimal revenue approximation for unit-demand and additive buyers, advancing multi-item mechanism design.
Contribution
It introduces a new revenue benchmark for multi-buyer mechanisms under buy-many constraints and demonstrates a simple sequential pricing mechanism achieves an $O(\log m)$ approximation.
Findings
Achieves $O(\log m)$ approximation for multi-buyer settings.
Matches the best possible approximation known from single-buyer results.
Develops novel technical tools for supply-constrained buy-many approximation and online contention resolution.
Abstract
A recent line of research has established a novel desideratum for designing approximately-revenue-optimal multi-item mechanisms, namely the buy-many constraint. Under this constraint, prices for different allocations made by the mechanism must be subadditive, implying that the price of a bundle cannot exceed the sum of prices of individual items it contains. This natural constraint has enabled several positive results in multi-item mechanism design bypassing well-established impossibility results. Our work addresses the main open question from this literature of extending the buy-many constraint to multiple buyer settings and developing an approximation. We propose a new revenue benchmark for multi-buyer mechanisms via an ex-ante relaxation that captures several different ways of extending the buy-many constraint to the multi-buyer setting. Our main result is that a simple sequential…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Voting Systems · Consumer Market Behavior and Pricing
