{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:42:20Z","timestamp":1774276940059,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>Quantum games extend classical game theory into the quantum realm by incorporating quantum players and quantum strategies. Two-player quantum games have been widely studied and applied, among other areas, in optimization and decision-making. In this work, we introduce, formalize and analyze a novel class of three-player quantum games, referred to as Proxy Quantum Games (PQGs). In this setting, one player, the Controller, influences or governs the strategic operations executed by a second player, the Proxy, who, in turn, competes directly against a third player, the Opponent. The strategic influence is implemented via controlled unitary operations, whereby the Proxy\u2019s available strategies are conditioned on the Controller\u2019s quantum state. We further generalize the PQG framework by incorporating multiple Controllers acting on a common Proxy, thereby enabling the study of higher-order strategic interactions and multi-agent influence structures. The objective under consideration is the maximization of the Controller\u2019s expected payoff, under various configurations of strategic control and entanglement. Comparative analyses are conducted between the PQG formulation and conventional multiplayer quantum games, highlighting key differences in strategic behavior and payoff distributions.<\/jats:p>","DOI":"10.1142\/s0129626425500148","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T10:12:41Z","timestamp":1765361561000},"source":"Crossref","is-referenced-by-count":1,"title":["Proxy Quantum Games"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0464-4842","authenticated-orcid":false,"given":"Georgios D.","family":"Varsamis","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece"},{"name":"National Centre for Scientific Research Demokritos, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2142-7670","authenticated-orcid":false,"given":"Ioannis","family":"Liliopoulos","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece"},{"name":"National Centre for Scientific Research Demokritos, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-1482-9970","authenticated-orcid":false,"given":"Hamed","family":"Mohammadbagherpoor","sequence":"additional","affiliation":[{"name":"IBM T. J. Watson Research Center, Yorktown Heights, New York, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7550-2377","authenticated-orcid":false,"given":"Andreas K.","family":"Kostopoulos","sequence":"additional","affiliation":[{"name":"EY Global Innovation Quantum Computing Lab, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5852-2257","authenticated-orcid":false,"given":"Kristin","family":"Milchanowski","sequence":"additional","affiliation":[{"name":"Bank of Montreal (BMO), Montreal, Quebec, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3322-3425","authenticated-orcid":false,"given":"Evangelos T.","family":"Karamatskos","sequence":"additional","affiliation":[{"name":"EY Global Innovation Quantum Computing Lab, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4941-0487","authenticated-orcid":false,"given":"Panagiotis","family":"Dimitrakis","sequence":"additional","affiliation":[{"name":"National Centre for Scientific Research Demokritos, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9772-0521","authenticated-orcid":false,"given":"Richard P.","family":"Padbury","sequence":"additional","affiliation":[{"name":"Bank of Montreal (BMO), Montreal, Quebec, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2079-5480","authenticated-orcid":false,"given":"Ioannis G.","family":"Karafyllidis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece"},{"name":"National Centre for Scientific Research Demokritos, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"S0129626425500148BIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.3077"},{"key":"S0129626425500148BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2009.05.007"},{"key":"S0129626425500148BIB003","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.1052"},{"key":"S0129626425500148BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-018-2082-8"},{"key":"S0129626425500148BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-021-00389-w"},{"key":"S0129626425500148BIB006","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.64.030301"},{"issue":"2","key":"S0129626425500148BIB007","first-page":"125","volume":"7","author":"de\u00a0Sousa P. B. M.","journal-title":"Quantum Inf. Process"},{"key":"S0129626425500148BIB008","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0036404"},{"key":"S0129626425500148BIB009","unstructured":"A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson and J. M. Gambetta, Quantum computing with qiskit."},{"key":"S0129626425500148BIB010","doi-asserted-by":"publisher","DOI":"10.1038\/246015a0"},{"key":"S0129626425500148BIB011","volume-title":"Quantum computation and quantum information 10th anniversary edition","author":"Nielsen M. 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