{"id":"https://openalex.org/W3045947153","doi":"https://doi.org/10.1007/s11128-020-02743-0","title":"A quantum approach to twice-repeated $$2\\times 2$$ game","display_name":"A quantum approach to twice-repeated $$2\\times 2$$ game","publication_year":2020,"publication_date":"2020-07-29","ids":{"openalex":"https://openalex.org/W3045947153","doi":"https://doi.org/10.1007/s11128-020-02743-0","mag":"3045947153"},"language":"en","primary_location":{"id":"doi:10.1007/s11128-020-02743-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11128-020-02743-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11128-020-02743-0.pdf","source":{"id":"https://openalex.org/S92819544","display_name":"Quantum Information Processing","issn_l":"1570-0755","issn":["1570-0755","1573-1332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11128-020-02743-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055099305","display_name":"Katarzyna Rycerz","orcid":"https://orcid.org/0000-0002-8032-7251"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Katarzyna Rycerz","raw_affiliation_strings":["Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakw, Poland","Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakw, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001779840","display_name":"Piotr Fra\u0327ckiewicz","orcid":"https://orcid.org/0000-0003-0034-9803"},"institutions":[{"id":"https://openalex.org/I4210092219","display_name":"Uniwersytet Pomorski w S\u0142upsku","ror":"https://ror.org/00h8nar58","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210092219"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Fr\u0105ckiewicz","raw_affiliation_strings":["Institute Exact and Technical Sciences, Pomeranian University, S\u0142upsk, Poland"],"affiliations":[{"raw_affiliation_string":"Institute Exact and Technical Sciences, Pomeranian University, S\u0142upsk, Poland","institution_ids":["https://openalex.org/I4210092219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055099305"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":{"value":2040,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2040,"currency":"EUR","value_usd":2690},"fwci":0.8336,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.72614871,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"19","issue":"8","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6201081275939941},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.5753343105316162},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5523480176925659},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5071792602539062},{"id":"https://openalex.org/keywords/dilemma","display_name":"Dilemma","score":0.5070059299468994},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4661712944507599},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.4578084647655487},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4193195700645447},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4125209152698517},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.346721887588501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2725848853588104},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18046650290489197},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1463364064693451},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09234094619750977},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0804203450679779}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6201081275939941},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5753343105316162},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5523480176925659},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5071792602539062},{"id":"https://openalex.org/C2778496695","wikidata":"https://www.wikidata.org/wiki/Q254128","display_name":"Dilemma","level":2,"score":0.5070059299468994},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4661712944507599},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.4578084647655487},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4193195700645447},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4125209152698517},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.346721887588501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2725848853588104},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18046650290489197},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1463364064693451},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09234094619750977},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0804203450679779},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11128-020-02743-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11128-020-02743-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11128-020-02743-0.pdf","source":{"id":"https://openalex.org/S92819544","display_name":"Quantum Information Processing","issn_l":"1570-0755","issn":["1570-0755","1573-1332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11128-020-02743-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11128-020-02743-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11128-020-02743-0.pdf","source":{"id":"https://openalex.org/S92819544","display_name":"Quantum Information Processing","issn_l":"1570-0755","issn":["1570-0755","1573-1332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information Processing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4699999988079071,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3377948470","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320324664","funder_display_name":"Akademia G\u00f3rniczo-Hutnicza im. Stanislawa Staszica"}],"funders":[{"id":"https://openalex.org/F4320324664","display_name":"Akademia G\u00f3rniczo-Hutnicza im. Stanislawa Staszica","ror":"https://ror.org/00bas1c41"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3045947153.pdf","grobid_xml":"https://content.openalex.org/works/W3045947153.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W245337057","https://openalex.org/W1409569118","https://openalex.org/W1422351985","https://openalex.org/W1580735130","https://openalex.org/W1704902497","https://openalex.org/W1818598351","https://openalex.org/W2019112050","https://openalex.org/W2121326822","https://openalex.org/W2149525981","https://openalex.org/W2330024298","https://openalex.org/W2793829449","https://openalex.org/W2806432762","https://openalex.org/W2953640035","https://openalex.org/W2954360440","https://openalex.org/W2963782485","https://openalex.org/W2964040263","https://openalex.org/W2995861475","https://openalex.org/W3037216216","https://openalex.org/W3038125555","https://openalex.org/W3101693170","https://openalex.org/W3102034668","https://openalex.org/W3102039651","https://openalex.org/W3121410382","https://openalex.org/W3122482575","https://openalex.org/W4234761190"],"related_works":["https://openalex.org/W1546864018","https://openalex.org/W2951363717","https://openalex.org/W2134613344","https://openalex.org/W2392657801","https://openalex.org/W4312141693","https://openalex.org/W1536009559","https://openalex.org/W1969185016","https://openalex.org/W2103821767","https://openalex.org/W2111030377","https://openalex.org/W2037619003"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"work":[2],"proposes":[3],"an":[4],"extension":[5],"of":[6,56,59,69,105,112],"the":[7,44,54,60,64,78,82,96,100,110,117],"well-known":[8],"Eisert\u2013Wilkens\u2013Lewenstein":[9],"scheme":[10,39],"for":[11],"playing":[12],"a":[13,28,70,74,92],"twice":[14],"repeated":[15],"$$2\\times":[16],"2$$":[17],"<mml:math":[18],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19],"<mml:mrow>":[20],"<mml:mn>2</mml:mn>":[21,23],"<mml:mo>\u00d7</mml:mo>":[22],"</mml:mrow>":[24],"</mml:math>":[25],"game":[26],"using":[27],"single":[29],"quantum":[30,75,93],"system":[31],"with":[32],"ten":[33],"maximally":[34],"entangled":[35],"qubits.":[36],"The":[37],"proposed":[38],"is":[40,91,103],"then":[41],"applied":[42],"to":[43],"Prisoner\u2019s":[45],"Dilemma":[46],"game.":[47],"Rational":[48],"strategy":[49],"profiles":[50],"are":[51],"examined":[52],"in":[53],"presence":[55],"limited":[57],"awareness":[58],"players.":[61],"In":[62],"particular,":[63],"paper":[65],"considers":[66],"two":[67],"cases":[68],"classical":[71,83,101],"player":[72,76,84,102],"against":[73],"game:":[77],"first":[79],"case":[80],"when":[81,99],"does":[85],"not":[86],"know":[87],"that":[88],"his":[89],"opponent":[90],"one":[94],"and":[95,116],"second":[97],"case,":[98],"aware":[104],"it.":[106],"To":[107],"this":[108],"end,":[109],"notion":[111],"unawareness":[113],"was":[114],"used,":[115],"extended":[118],"Nash":[119],"equilibria":[120],"were":[121],"determined.":[122]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}