{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:44:11Z","timestamp":1740109451439,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state <jats:italic>x<\/jats:italic> at most one of which could differ from the point mass <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta (x)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b4<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>x<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Their result is extended here to a family of two-person, zero-sum stochastic games in which each player is similarly restricted. For these games we show that player 1 always has a pure optimal stationary strategy and that player 2 has a pure <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03f5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-optimal stationary strategy for every <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon &gt; 0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03f5<\/mml:mi>\n                    <mml:mo>&gt;<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. However, player 2 has no optimal strategy in general. A generalization to <jats:italic>n<\/jats:italic>-person games is formulated and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03f5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-equilibria are constructed.<\/jats:p>","DOI":"10.1007\/s00182-021-00762-4","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T12:02:40Z","timestamp":1616587360000},"page":"559-579","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Discrete stop-or-go games"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-4615","authenticated-orcid":false,"given":"J\u00e1nos","family":"Flesch","sequence":"first","affiliation":[]},{"given":"Arkadi","family":"Predtetchinski","sequence":"additional","affiliation":[]},{"given":"William","family":"Sudderth","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"key":"762_CR1","volume-title":"Great expectations: the theory of optimal stopping","author":"YS Chow","year":"1971","unstructured":"Chow YS, Robbins H, Siegmund D (1971) Great expectations: the theory of optimal stopping. 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