{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:33:17Z","timestamp":1757313197707,"version":"3.41.2"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["SFB 901"],"award-info":[{"award-number":["SFB 901"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> Nash\u2019s [1953] demand game models the second step in a \u201ctwo-move game\u201d that formalizes his \u201cNegotiation Model\u201d. Nash claimed for any two-person bargaining game [Formula: see text] the existence of a unique stable equilibrium of its associated second move demand game that by its payoff vector supports the symmetric Nash solution of that bargaining game. <\/jats:p><jats:p> Nash\u2019s negotiation game is considered the first contribution to the Nash program. Only weaker versions of stability than that claimed by Nash have been formally proven later by other authors. However, Nash\u2019s request for \u201cstudying the relative stabilities\u201d of the demand game\u2019s equilibria has never been complied with. By performing that task, we establish analogous stability results for all generalized Nash solutions and thereby disprove Nash\u2019s \u201cunique stability\u201d claim. <\/jats:p><jats:p> Furthermore, we explain the impact of our result on the Nash solution with endogenous variable threats (NBWT) of the two move negotiation game, which is defined as the symmetric Nash solution of that bargaining game [Formula: see text] whose status quo point [Formula: see text] is the unique payoff vector of the payoff-equivalent equilibria of the first move threat game. <\/jats:p>","DOI":"10.1142\/s0219198924500129","type":"journal-article","created":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T08:47:45Z","timestamp":1717750065000},"source":"Crossref","is-referenced-by-count":1,"title":["Nash Smoothing on the Test Bench: H\u03b1-Essential Equilibria"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2518-127X","authenticated-orcid":false,"given":"Papatya","family":"Duman","sequence":"first","affiliation":[{"name":"Department of Economics, Paderborn University, Paderborn 33098, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9827-6424","authenticated-orcid":false,"given":"Walter","family":"Trockel","sequence":"additional","affiliation":[{"name":"Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld 33615, Germany"}]}],"member":"219","published-online":{"date-parts":[[2024,7,30]]},"reference":[{"key":"S0219198924500129BIB001","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA11711"},{"key":"S0219198924500129BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01763116"},{"key":"S0219198924500129BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00199-018-1111-2"},{"key":"S0219198924500129BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2017.10.007"},{"key":"S0219198924500129BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-20181-5_1"},{"key":"S0219198924500129BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.1998.2505"},{"volume-title":"The Economics of Bargaining","year":"1987","author":"Binmore K.","key":"S0219198924500129BIB007"},{"volume-title":"The Economics of Bargaining","year":"1987","author":"Binmore K.","key":"S0219198924500129BIB008"},{"key":"S0219198924500129BIB009","doi-asserted-by":"publisher","DOI":"10.2307\/2938376"},{"key":"S0219198924500129BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-96978-2"},{"key":"S0219198924500129BIB011","first-page":"635","volume":"26","author":"Haake C.-J.","year":"2022","journal-title":"Rev. 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