{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:18Z","timestamp":1759335798593,"version":"build-2065373602"},"reference-count":26,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research"],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> Computing Nash Equilibria as Pareto Points <\/jats:p><jats:p> Recent work by Feinstein and Rudloff (\u201cCharacterizing and Computing the Set of Nash Equilibria via Vector Optimization\u201d) proved that it is possible to characterize the set of all Nash equilibria as the set of all Pareto optimal solutions of a certain vector optimization problem. \u201cApproximating the Set of Nash Equilibria for Convex Games\u201d by Feinstein, Hey, and Rudloff expands on this result to demonstrate that a comparable relation holds between the set of all approximate Nash equilibria and approximate Pareto solutions of a specific vector optimization problem. This characterization holds for all noncooperative games but opens a new way of computing Nash equilibria using techniques and algorithms from convex vector optimization. A sandwich property is proven in which the computed set of approximate Pareto solutions is bounded between the set of true Nash equilibria and the set of all approximate Nash equilibria with controlled error. <\/jats:p>","DOI":"10.1287\/opre.2023.0541","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T11:08:53Z","timestamp":1728558533000},"page":"2729-2743","source":"Crossref","is-referenced-by-count":0,"title":["Approximating the Set of Nash Equilibria for Convex Games"],"prefix":"10.1287","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6733-5724","authenticated-orcid":false,"given":"Zachary","family":"Feinstein","sequence":"first","affiliation":[{"name":"Stevens Institute of Technology, School of Business, Hoboken, New Jersey 07030"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Niklas","family":"Hey","sequence":"additional","affiliation":[{"name":"Vienna University of Economics and Business, Institute for Statistics and Mathematics, A-1020 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1675-5451","authenticated-orcid":false,"given":"Birgit","family":"Rudloff","sequence":"additional","affiliation":[{"name":"Vienna University of Economics and Business, Institute for Statistics and Mathematics, A-1020 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582157"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2022.10.036"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1086\/261003"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-010-0218-6"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2006.03.004"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1007\/s40505-022-00228-0"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2023.2457"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-006-8718-0"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2011.09.007"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17005-8"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-021-01111-1"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2016.0302"},{"issue":"2","key":"B14","first-page":"391","volume":"20","author":"Kutateladze SS","year":"1979","journal-title":"Soviet Math. 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