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We then define the concept of <jats:italic>sequentially 0-perfect<\/jats:italic> absorption paths, which are shown to be limits of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-equilibrium strategy profiles as <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> goes to 0. We establish that all quitting games that do not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) have a sequentially 0-perfect absorption path. Finally, we prove the existence of sequentially 0-perfect absorption paths in a new class of quitting games.\n<\/jats:p>","DOI":"10.1007\/s10107-022-01807-6","type":"journal-article","created":{"date-parts":[[2022,4,22]],"date-time":"2022-04-22T16:02:53Z","timestamp":1650643373000},"page":"735-762","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Absorption paths and equilibria in quitting games"],"prefix":"10.1007","volume":"203","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3896-4131","authenticated-orcid":false,"given":"Galit","family":"Ashkenazi-Golan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilia","family":"Krasikov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Catherine","family":"Rainer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eilon","family":"Solan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,22]]},"reference":[{"key":"1807_CR1","doi-asserted-by":"crossref","unstructured":"Ashkenazi-Golan, G., Krasikov, I., Rainer, R., Solan, E.: Algorithms for continuous equilibria in quitting games (2022) (in preparation)","DOI":"10.1007\/s10107-022-01807-6"},{"key":"1807_CR2","volume-title":"Viability Theory","author":"J-P Aubin","year":"1991","unstructured":"Aubin, J.-P.: Viability Theory. 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