An α-regret analysis of Adversarial Bilateral Trade

Yossi Azar, Amos Fiat, Federico Fusco

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study sequential bilateral trade where sellers and buyers valuations are completely arbitrary (i.e., determined by an adversary). Sellers and buyers are strategic agents with private valuations for the good and the goal is to design a mechanism that maximizes efficiency (or gain from trade) while being incentive compatible, individually rational and budget balanced. In this paper we consider gain from trade which is harder to approximate than social welfare. We consider a variety of feedback scenarios and distinguish the cases where the mechanism posts one price and when it can post different prices for buyer and seller. We show several surprising results about the separation between the different scenarios. In particular, we show that (a) it is impossible to achieve sublinear α-regret for any α < 2, (b) but with full feedback sublinear 2-regret is achievable (c) with a single price and partial feedback one cannot get sublinear α regret for any constant α (d) nevertheless, posting two prices even with one-bit feedback achieves sublinear 2-regret, and (e) there is a provable separation in the 2-regret bounds between full and partial feedback.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
EditorsS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
PublisherNeural information processing systems foundation
ISBN (Electronic)9781713871088
StatePublished - 2022
Event36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States
Duration: 28 Nov 20229 Dec 2022

Publication series

NameAdvances in Neural Information Processing Systems
Volume35
ISSN (Print)1049-5258

Conference

Conference36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/TerritoryUnited States
CityNew Orleans
Period28/11/229/12/22

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