{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T09:10:26Z","timestamp":1778231426410,"version":"3.51.4"},"reference-count":24,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>We present the following analog of O\u2019Neill\u2019s theorem (O\u2019Neill B (1953) Essential sets and fixed points. Amer. J. Math. 75(3):497\u2013509 (theorem 5.2)) for finite games. Let [Formula: see text] be the components of Nash equilibria of a finite normal-form game G. For each i, let [Formula: see text] be the index of [Formula: see text]. For each [Formula: see text], there exist pairwise disjoint neighborhoods [Formula: see text] of the components such that for any choice of finitely many distinct completely mixed strategy profiles [Formula: see text] for each [Formula: see text] and numbers [Formula: see text] such that [Formula: see text], there exists a normal-form game [Formula: see text] obtained from G by adding duplicate strategies and an [Formula: see text]-perturbation [Formula: see text] of [Formula: see text] such that the set of equilibria of [Formula: see text] is [Formula: see text], where for each i, j, (1) [Formula: see text] is equivalent to the profile [Formula: see text] and (2) the index [Formula: see text] equals [Formula: see text].<\/jats:p>\n                  <jats:p>Funding: L. Pahl acknowledges financial support from the Hausdorff Center for Mathematics [Deutsche Forschungsgemeinschaft Project 390685813].<\/jats:p>","DOI":"10.1287\/moor.2022.0304","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T12:16:49Z","timestamp":1749039409000},"page":"1514-1537","source":"Crossref","is-referenced-by-count":0,"title":["O\u2019Neill\u2019s Theorem for Games"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3410-3054","authenticated-orcid":false,"given":"Srihari","family":"Govindan","sequence":"first","affiliation":[{"name":"Department of Economics, University of Rochester, New York 14627"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4898-2424","authenticated-orcid":false,"given":"Rida","family":"Laraki","sequence":"additional","affiliation":[{"name":"Moroccan Center for Game Theory, University Mohammed VI Polytechnic (UM6P), Rabat 43150, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0268-371X","authenticated-orcid":false,"given":"Lucas","family":"Pahl","sequence":"additional","affiliation":[{"name":"School of Economics, University of Sheffield, Sheffield S10 2TN, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03718-8"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12971-1"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.2000.2669"},{"key":"B4","doi-asserted-by":"crossref","unstructured":"Eaves BC, Lemke CE (1981) Equivalence of LCP and PLS.\n                      Math. 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