{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T07:18:36Z","timestamp":1760080716879,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001786","name":"The University of Adelaide","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001786","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player\u2019s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players\u2019 choices to specific spatial trajectories. We show that for players\u2019 directional choices for which the Bell-CHSH inequality is violated, the players\u2019 payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.<\/jats:p>","DOI":"10.1007\/s11128-022-03526-5","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T21:02:51Z","timestamp":1655240571000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Two-player quantum games: When player strategies are via directional choices"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5221-9384","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0945-2674","authenticated-orcid":false,"given":"Derek","family":"Abbott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"3526_CR1","doi-asserted-by":"publisher","first-page":"1052","DOI":"10.1103\/PhysRevLett.82.1052","volume":"82","author":"DA Meyer","year":"1999","unstructured":"Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"3526_CR2","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1103\/PhysRevLett.83.3077","volume":"83","author":"J Eisert","year":"1999","unstructured":"Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"3526_CR3","doi-asserted-by":"publisher","first-page":"2543","DOI":"10.1080\/09500340008232180","volume":"47","author":"J Eisert","year":"2000","unstructured":"Eisert, J., Wilkens, M.: Quantum games. J. Mod. Opt. 47, 2543 (2000)","journal-title":"J. Mod. Opt."},{"key":"3526_CR4","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1023\/A:1018868326838","volume":"29","author":"L Vaidman","year":"1999","unstructured":"Vaidman, L.: Variations on the theme of the Greenberger-Horne-Zeilinger proof. Found. Phys. 29, 615\u2013630 (1999)","journal-title":"Found. Phys."},{"key":"3526_CR5","doi-asserted-by":"publisher","DOI":"10.1093\/actrade\/9780199218462.001.0001","volume-title":"Game Theory: A Very Short Introduction","author":"K Binmore","year":"2007","unstructured":"Binmore, K.: Game Theory: A Very Short Introduction. Oxford University Press, New York (2007)"},{"key":"3526_CR6","volume-title":"Games Information: An Introduction to Game Theory","author":"E Rasmusen","year":"2001","unstructured":"Rasmusen, E.: Games Information: An Introduction to Game Theory, 3rd edn. Blackwell, Oxford (2001)","edition":"3"},{"key":"3526_CR7","volume-title":"An Introduction to Game Theory","author":"MJ Osborne","year":"2003","unstructured":"Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, New York (2003)"},{"key":"3526_CR8","volume-title":"Quantum Theory: Concepts and Methods","author":"A Peres","year":"1995","unstructured":"Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1995)"},{"key":"3526_CR9","unstructured":"Kolokoltsov, V.: Quantum games: a survey for mathematicians, arxiv: abs\/1909.04466"},{"key":"3526_CR10","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s11128-018-2082-8","volume":"17","author":"FS Khan","year":"2018","unstructured":"Khan, F.S., Solmeyer, N., Balu, R., et al.: Quantum games: a review of the history, current state, and interpretation. Quantum Inf. Process. 17, 309 (2018)","journal-title":"Quantum Inf. Process."},{"key":"3526_CR11","unstructured":"The URL\u00a0https:\/\/scholar.google.com.au\/citations?user=wkfPcaQAAAAJ &hl=en contains an extensive list\u00a0of publications\u00a0on\u00a0the subject\u00a0of\u00a0quantum\u00a0games"},{"key":"3526_CR12","doi-asserted-by":"crossref","unstructured":"Zhang, S.: Quantum strategic game theory, Proceeding ITCS \u201912, Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp 39-59, Cambridge, Massachusetts\u2014January 08\u201310 (2012)","DOI":"10.1145\/2090236.2090241"},{"key":"3526_CR13","doi-asserted-by":"publisher","first-page":"2057","DOI":"10.1038\/ncomms3057","volume":"4","author":"N Brunner","year":"2013","unstructured":"Brunner, N., Linden, N.: Bell nonlocality and Bayesian game theory. Nat. Commun. 4, 2057 (2013)","journal-title":"Nat. Commun."},{"key":"3526_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.020401","volume":"114","author":"A Pappa","year":"2015","unstructured":"Pappa, A., Kumar, N., Lawson, T., Santha, M., Zhang, S., Diamanti, E., Kerenidis, I.: Nonlocality and conflicting interest games. Phys. Rev. Lett. 114, 020401 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"3526_CR15","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s11128-019-2519-8","volume":"19","author":"K Ikeda","year":"2020","unstructured":"Ikeda, K.: Foundation of quantum optimal transport and applications. Quantum Inf. Process. 19, 25 (2020)","journal-title":"Quantum Inf. Process."},{"key":"3526_CR16","unstructured":"Aoki, S., Ikeda, K.: Repeated Quantum Games and Strategic Efficiency, arxiv: abs\/2005.05588"},{"key":"3526_CR17","unstructured":"Aoki, S., Ikeda, K.: Theory of Quantum Games and Quantum Economic Behavior, arxiv: abs\/2010.14098"},{"key":"3526_CR18","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/s11128-020-02798-z","volume":"19","author":"MHM Passos","year":"2020","unstructured":"Passos, M.H.M., Tiago, G.S.G.P., de Ponte, M.A., et al.: Experimental observation of phase-transition-like behavior in an optical simulation of single-qubit game. Quantum Inf. Process. 19, 302 (2020)","journal-title":"Quantum Inf. Process."},{"key":"3526_CR19","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/s11128-019-2502-4","volume":"19","author":"AC Santos","year":"2020","unstructured":"Santos, A.C.: Entanglement and coherence in quantum prisoner\u2019s dilemma. Quantum Inf. Process. 19, 13 (2020)","journal-title":"Quantum Inf. Process."},{"key":"3526_CR20","doi-asserted-by":"publisher","first-page":"305301","DOI":"10.1088\/1751-8113\/47\/30\/305301","volume":"47","author":"P Frackiewicz","year":"2014","unstructured":"Frackiewicz, P.: Quantum signaling game. J. Phys. A: Math. Theor. 47, 305301 (2014)","journal-title":"J. Phys. A: Math. Theor."},{"key":"3526_CR21","doi-asserted-by":"publisher","first-page":"024306","DOI":"10.1103\/PhysRevA.66.024306","volume":"66","author":"SJ van Enk","year":"2002","unstructured":"van Enk, S.J., Pike, R.: Classical rules in quantum games. Phys. Rev. A 66, 024306 (2002)","journal-title":"Phys. Rev. A"},{"key":"3526_CR22","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195","volume":"1","author":"J Bell","year":"1964","unstructured":"Bell, J.: On the Einstein\u2013Podolsky\u2013Rosen paradox. Physics 1, 195\u2013200 (1964)","journal-title":"Physics"},{"key":"3526_CR23","volume-title":"Speakable and Unspeakable in Quantum Mechanics","author":"J Bell","year":"1987","unstructured":"Bell, J.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)"},{"key":"3526_CR24","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1103\/RevModPhys.38.447","volume":"38","author":"J Bell","year":"1966","unstructured":"Bell, J.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447\u2013452 (1966)","journal-title":"Rev. Mod. Phys."},{"key":"3526_CR25","doi-asserted-by":"publisher","first-page":"1804","DOI":"10.1103\/PhysRevLett.49.1804","volume":"49","author":"A Aspect","year":"1982","unstructured":"Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell\u2019s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804\u20131807 (1982)","journal-title":"Phys. Rev. Lett."},{"key":"3526_CR26","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1103\/PhysRevLett.23.880","volume":"23","author":"JF Clauser","year":"1969","unstructured":"Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880\u2013884 (1969)","journal-title":"Phys. Rev. Lett."},{"key":"3526_CR27","doi-asserted-by":"publisher","first-page":"5873","DOI":"10.1088\/0305-4470\/37\/22\/012","volume":"37","author":"A Iqbal","year":"2004","unstructured":"Iqbal, A., Weigert, S.: Quantum correlation games. J. Phys. A: Math. Gen. 37, 5873\u20135885 (2004)","journal-title":"J. Phys. A: Math. Gen."},{"key":"3526_CR28","doi-asserted-by":"publisher","first-page":"6564","DOI":"10.1016\/j.physleta.2008.09.026","volume":"372","author":"A Iqbal","year":"2008","unstructured":"Iqbal, A., Cheon, T., Abbott, D.: Probabilistic analysis of three-player symmetric quantum games played using the Einstein\u2013Podolsky\u2013Rosen\u2013Bohm setting. Phys. Lett. A 372, 6564 (2008)","journal-title":"Phys. Lett. A"},{"key":"3526_CR29","doi-asserted-by":"publisher","first-page":"014803","DOI":"10.1143\/JPSJ.78.014803","volume":"78","author":"A Iqbal","year":"2009","unstructured":"Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Phys. Soc. Jpn. 78, 014803 (2009)","journal-title":"J. Phys. Soc. Jpn."},{"issue":"7","key":"3526_CR30","doi-asserted-by":"publisher","first-page":"e21623","DOI":"10.1371\/journal.pone.0021623","volume":"6","author":"JM Chappell","year":"2011","unstructured":"Chappell, J.M., Iqbal, A., Abbott, D.: Analyzing three-player quantum games in an EPR type setup. PLoS ONE 6(7), e21623 (2011)","journal-title":"PLoS ONE"},{"issue":"1","key":"3526_CR31","doi-asserted-by":"publisher","first-page":"e29015","DOI":"10.1371\/journal.pone.0029015","volume":"7","author":"JM Chappell","year":"2012","unstructured":"Chappell, J.M., Iqbal, A., Abbott, D.: Analysis of two-player quantum games in an EPR setting using geometric algebra. PLoS ONE 7(1), e29015 (2012)","journal-title":"PLoS ONE"},{"key":"3526_CR32","doi-asserted-by":"publisher","first-page":"3155","DOI":"10.1016\/j.physleta.2010.05.062","volume":"374","author":"A Iqbal","year":"2010","unstructured":"Iqbal, A., Abbott, D.: Constructing quantum games from a system of Bell\u2019s inequalities. Phys. Lett. A 374, 3155\u20133163 (2010)","journal-title":"Phys. Lett. A"},{"key":"3526_CR33","doi-asserted-by":"crossref","unstructured":"Iqbal, A., Abbott, D.: A game theoretical perspective on the quantum probabilities associated with a GHZ state. Quantum Inf. Process. 17, Art. No. 313 (2018)","DOI":"10.1007\/s11128-018-2083-7"},{"key":"3526_CR34","doi-asserted-by":"publisher","first-page":"069801","DOI":"10.1103\/PhysRevLett.87.069801","volume":"87","author":"SC Benjamin","year":"2001","unstructured":"Benjamin, S.C., Hayden, Patrick M.: Comment on Quantum games and quantum strategies. Phys. Rev. Lett. 87, 069801 (2001)","journal-title":"Phys. Rev. Lett."},{"issue":"5\u20136","key":"3526_CR35","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.physleta.2006.11.044","volume":"363","author":"AP Flitney","year":"2007","unstructured":"Flitney, A.P., Hollenberg, L.C.L.: Nash equilibria in quantum games with generalized two-parameter strategies. Phys. Lett. A 363(5\u20136), 381\u2013388 (2007)","journal-title":"Phys. Lett. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03526-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03526-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03526-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T16:52:59Z","timestamp":1656607979000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03526-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":35,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["3526"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03526-5","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2022,6]]},"assertion":[{"value":"3 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"212"}}