{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:58Z","timestamp":1760241718494,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2016\/23\/D\/ST1\/01557"],"award-info":[{"award-number":["2016\/23\/D\/ST1\/01557"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Games with unawareness model strategic situations in which players\u2019 perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as well as the players may have a restricted view about the number of players participating in the game. The aim of the paper is to introduce this notion into theory of quantum games. We focus on games in strategic form and Eisert\u2013Wilkens\u2013Lewenstein type quantum games. It is shown that limiting a player\u2019s perception in the game enriches the structure of the quantum game substantially and allows the players to obtain results that are unattainable when the game is played in a quantum way by means of previously used methods.<\/jats:p>","DOI":"10.3390\/e20080555","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T11:32:07Z","timestamp":1532604727000},"page":"555","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Quantum Games with Unawareness"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0034-9803","authenticated-orcid":false,"given":"Piotr","family":"Fr\u0105ckiewicz","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Pomeranian University, 76-200 Slupsk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01448847","article-title":"Zur Theorie der Gesellschaftsspiele","volume":"100","year":"1928","journal-title":"Math. Ann."},{"key":"ref_2","unstructured":"Von Neumann, J., and Morgenstern, O. (1944). Theory of Games and Economic Behavior, Princeton University Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1103\/PhysRevLett.82.1052","article-title":"Quantum strategies","volume":"82","author":"Meyer","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1007\/s11128-012-0515-3","article-title":"Evolutionarily stable sets in quantum penny flip games","volume":"12","author":"Yu","year":"2013","journal-title":"Quantum Inf. Process"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"050303","DOI":"10.1088\/0256-307X\/27\/5\/050303","article-title":"Evolutionarily stable strategies in quantum Hawk-Dove game","volume":"27","author":"Nawaz","year":"2010","journal-title":"Chin. Phys. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0375-9601(01)00082-2","article-title":"Evolutionarily stable strategies in quantum games","volume":"280","author":"Iqbal","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1007\/s10773-010-0483-2","article-title":"Arbiter as a third man in classical and quantum games","volume":"49","author":"Pykacz","year":"2010","journal-title":"Int. J. Theor. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1142\/S0219749905000724","article-title":"Correlated equilibria of classical strategic games with quantum signals","volume":"3","year":"2005","journal-title":"Int. J. Quantum Inf."},{"key":"ref_9","first-page":"846","article-title":"Full characterization of quantum correlated equilibria","volume":"13","author":"Wei","year":"2013","journal-title":"Quantum Inf. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Fr\u0105ckiewicz, P. (2016, January 18\u201322). On quantum game approach to correlated equilibrium. Proceedings of the 4th Global Virtual Conference, Zilina, Slovakia.","DOI":"10.18638\/gv.2016.4.1.738"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1250048","DOI":"10.1142\/S0219749912500487","article-title":"Quantum information approach to normal representation of extensive games","volume":"10","year":"2012","journal-title":"Int. J. Quantum Inf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3248","DOI":"10.1007\/s10773-013-1633-0","article-title":"Quantum information approach to the ultimatum game","volume":"53","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0375-9601(02)00893-9","article-title":"Quantum repeated games","volume":"300","author":"Iqbal","year":"2002","journal-title":"Phys. Lett. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"085307","DOI":"10.1088\/1751-8113\/45\/8\/085307","article-title":"Quantum repeated games revisited","volume":"45","year":"2012","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0375-9601(02)00003-8","article-title":"Quantum cooperative games","volume":"293","author":"Iqbal","year":"2002","journal-title":"Phys. Lett. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4395","DOI":"10.1007\/s11128-015-1144-4","article-title":"Improving the payoffs of cooperators in three-player cooperative game using weak measurements","volume":"14","author":"Liao","year":"2015","journal-title":"Quantum Inf. Process"},{"key":"ref_17","unstructured":"Feinberg, Y. (2012). Games with Unawareness, Stanford Graduate School of Business. Working Paper No. 2122."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Fr\u0105ckiewicz, P. (arXiv, 2018). Quantum Penny Flip game with unawareness, arXiv.","DOI":"10.1007\/s11128-018-2111-7"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"286","DOI":"10.2307\/1969529","article-title":"Non-Cooperative Games","volume":"54","author":"Nash","year":"1951","journal-title":"Ann. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3077","DOI":"10.1103\/PhysRevLett.83.3077","article-title":"Quantum games and quantum strategies","volume":"83","author":"Eisert","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"030301","DOI":"10.1103\/PhysRevA.64.030301","article-title":"Multiplayer quantum games","volume":"64","author":"Benjamin","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fr\u0105ckiewicz, P. (2016). Strong isomorphism in Eisert-Wilkens-Lewenstein type quantum games. Adv. Math. Phys.","DOI":"10.1155\/2016\/4180864"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Maschler, M., Solan, E., and Zamir, S. (2013). Game Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511794216"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4423","DOI":"10.1090\/S0002-9939-2011-10838-4","article-title":"Nash equilibria in quantum games","volume":"139","author":"Landsburg","year":"2011","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s10623-009-9290-2","article-title":"Unitary designs and codes","volume":"53","author":"Roy","year":"2009","journal-title":"Des. Codes Cryptogr."},{"key":"ref_26","unstructured":"Kaznatcheev, A. (2010, May 09). Structure of Exact and Approximate Unitary T-Designs. Available online: http:\/\/www.cs.mcgill.ca\/~akazna\/kaznatcheev20100509.pdf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"069801","DOI":"10.1103\/PhysRevLett.87.069801","article-title":"Comment on \u201cQuantum Games and Quantum Strategies\u201d","volume":"87","author":"Benjamin","year":"2001","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/555\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:14:37Z","timestamp":1760195677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,26]]},"references-count":27,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["e20080555"],"URL":"https:\/\/doi.org\/10.3390\/e20080555","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,7,26]]}}}