{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T02:44:42Z","timestamp":1782787482491,"version":"3.54.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:00:00Z","timestamp":1744156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:00:00Z","timestamp":1744156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006470","name":"Aristotle University of Thessaloniki","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006470","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2026,7]]},"abstract":"Abstract<\/jats:title>\n \n We study the following game. Three players start with initial capitals of\n \n \n $$s_{1},s_{2},s_{3}$$<\/jats:tex-math>\n \n \n \n s<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n s<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n s<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n dollars; in each round player\n \n \n $$P_{m}$$<\/jats:tex-math>\n \n \n P<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is selected with probability\n \n \n $$\\frac{1}{3}$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n 3<\/mml:mn>\n <\/mml:mfrac>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ; then\n he<\/jats:italic>\n selects player\n \n \n $$P_{n}$$<\/jats:tex-math>\n \n \n P<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and they play a game in which\n \n \n $$P_{m}$$<\/jats:tex-math>\n \n \n P<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n wins from (resp. loses to)\n \n \n $$P_{n}$$<\/jats:tex-math>\n \n \n P<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n one dollar with probability\n \n \n $$p_{mn}$$<\/jats:tex-math>\n \n \n p<\/mml:mi>\n \n mn<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (resp.\n \n \n $$p_{nm}=1-p_{mn}$$<\/jats:tex-math>\n \n \n \n p<\/mml:mi>\n \n nm<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n =<\/mml:mo>\n 1<\/mml:mn>\n -<\/mml:mo>\n \n p<\/mml:mi>\n \n mn<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ). When a player loses all his capital he drops out; the game continues until a single player wins by collecting everybody\u2019s money. This is a \u201cstrategic\u201d version of the classical Gambler\u2019s Ruin game. It seems reasonable that a player may improve his winning probability by judicious selection of which opponent to engage in each round. We formulate the situation as a\n stochastic game<\/jats:italic>\n and prove that it has at least one Nash equilibrium in stationary deterministic strategies.\n <\/jats:p>","DOI":"10.1007\/s13235-025-00641-7","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T18:35:06Z","timestamp":1744223706000},"page":"866-883","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three-Gambler Ruin Game: A Game Theoretic Analysis"],"prefix":"10.1007","volume":"16","author":[{"given":"Athanasios","family":"Kehagias","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Georgios","family":"Gkyzis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anastasios","family":"Karakoulakis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aris","family":"Kyprianidis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"key":"641_CR1","doi-asserted-by":"crossref","unstructured":"Amano K et al (2001) On a generalized ruin problem. 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