{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T23:28:56Z","timestamp":1783985336385,"version":"3.55.0"},"reference-count":23,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research"],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:p> Budgets play a significant role in ad markets that implement sequential auctions such as those hosted by internet companies. In \u201cMultiplicative Pacing Equilibria in Auction Markets,\u201d the authors look at pacing in an ad marketplace using the lens of game theory. The goal is understanding how bids must be shaded to maximize advertiser welfare, at equilibrium. Motivated by the real-world auction mechanism, they construct a game where advertisers in the auctions choose a multiplicative factor not larger than 1 to possibly reduce their bids and best respond to the other advertisers. The article studies the theoretical properties of the game such as existence and uniqueness of equilibria, offers an exact algorithm to compute them, connects the game to well-known abstractions such as Fisher markets, and performs a computational study with real-world-inspired instances. The main insights are that the solutions to the studied game can be used to improve the outcomes achieved by a closer-to-reality dynamic pacing algorithm and that buyers do not have an incentive to misreport bids or budgets when there are enough participants in the auction. <\/jats:p>","DOI":"10.1287\/opre.2021.2167","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T20:10:07Z","timestamp":1639426207000},"page":"963-989","source":"Crossref","is-referenced-by-count":30,"title":["Multiplicative Pacing Equilibria in Auction Markets"],"prefix":"10.1287","volume":"70","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-1899-7884","authenticated-orcid":false,"given":"Vincent","family":"Conitzer","sequence":"first","affiliation":[{"name":"Econorithms, LLC, Durham, North Carolina 27708;"},{"name":"Computer Science Department, Duke University, Durham, North Carolina 27708;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-9009-8683","authenticated-orcid":false,"given":"Christian","family":"Kroer","sequence":"additional","affiliation":[{"name":"Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027;"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Sodomka","sequence":"additional","affiliation":[{"name":"Core Data Science, Facebook Inc., Menlo Park, California 94025"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-6380-1516","authenticated-orcid":false,"given":"Nicolas E.","family":"Stier-Moses","sequence":"additional","affiliation":[{"name":"Core Data Science, Facebook Inc., Menlo Park, California 94025"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"109","reference":[{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2018.3207"},{"issue":"1","key":"B5","volume":"10","author":"Ashlagi I","year":"2010","journal-title":"B. 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