{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T10:54:41Z","timestamp":1762253681996,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T00:00:00Z","timestamp":1611705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671284"],"award-info":[{"award-number":["11671284"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.<\/jats:p>","DOI":"10.3390\/e23020154","type":"journal-article","created":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T06:10:54Z","timestamp":1611727854000},"page":"154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Tripartite Dynamic Zero-Sum Quantum Games"],"prefix":"10.3390","volume":"23","author":[{"given":"Hui-Min","family":"Cheng","sequence":"first","affiliation":[{"name":"Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming-Xing","family":"Luo","sequence":"additional","affiliation":[{"name":"Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"041003","DOI":"10.1103\/RevModPhys.89.041003","article-title":"Colloquium: Quantum coherence as a resource","volume":"89","author":"Streltsov","year":"2017","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195","article-title":"On the Einstein Podolsky Rosen paradox","volume":"1","author":"Bell","year":"1964","journal-title":"Physics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1103\/PhysRevLett.23.880","article-title":"Proposed experiment to test local hidden-variable theories","volume":"23","author":"Clauser","year":"1969","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","first-page":"394","article-title":"Quantum Game Theory","volume":"51","author":"Landsburg","year":"2004","journal-title":"Not. Am. Math. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"030301","DOI":"10.1103\/PhysRevA.64.030301","article-title":"Multi-player quantum games","volume":"64","author":"Benjamin","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.physleta.2008.12.003","article-title":"Equivalence between Bell inequalities and quantum minority games","volume":"373","author":"Flitney","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"022305","DOI":"10.1103\/PhysRevA.93.022305","article-title":"Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement","volume":"93","author":"Murta","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1038\/s41534-019-0203-6","article-title":"A nonlocal game for witnessing quantum networks","volume":"5","author":"Luo","year":"2019","journal-title":"NPJ Quantum Inf."},{"key":"ref_9","unstructured":"Cleve, R., Hoyer, P., Toner, B., and Watrous, J. (2004, January 21\u201324). Consequences and limits of nonlocal strategies. Proceedings of the 19th IEEE Conference on Computational Complexity (CCC2004), Amherst, MA, USA."},{"key":"ref_10","first-page":"1","article-title":"Large violation of Bell inequalities with low entanglement","volume":"11","author":"Junge","year":"2011","journal-title":"Commun. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00220-012-1642-5","article-title":"Explicit lower and upper bounds on the entangled value of multiplayer XOR games","volume":"321","author":"Vidick","year":"2013","journal-title":"Commun. Math. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2799560","article-title":"Quantum XOR games","volume":"7","author":"Regev","year":"2015","journal-title":"ACM Trans. Comput. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3207","DOI":"10.1137\/090772885","article-title":"Unique games with entangled provers are easy","volume":"39","author":"Kempe","year":"2010","journal-title":"SIAM J. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00037-015-0098-3","article-title":"A parallel repetition theorem for entangled projection games","volume":"24","author":"Dinur","year":"2013","journal-title":"Comput. Complex."},{"key":"ref_15","unstructured":"Yuen, H. (2016, January 11\u201315). A Parallel Repetition Theorem for All Entangled Games. Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), Rome, Italy."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jain, R., Pereszlenyi, A., and Yao, P. (2014, January 11\u201313). A parallel repetition theorem for entangled two-player one-round games under product distributions. Proceedings of the CCC\u201914, 2014 IEEE 29th Conference on Computational Complexity, Vancouver, BC, Canada.","DOI":"10.1109\/CCC.2014.29"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., and Kalai, Y.T. (2012). A Parallel Repetition Theorem for Leakage Resilience. TCC\u201912, Proceedings of the 9th International Conference on Theory of Cryptography, Taormina, Sicily, Italy, 19\u201321 March 2012, Springer.","DOI":"10.1007\/978-3-642-28914-9_14"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1103\/PhysRevLett.67.661","article-title":"Quantum cryptography based on Bell\u2019s theorem","volume":"67","author":"Ekert","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","first-page":"031006","article-title":"Device-Independent Quantum Key Distribution with Local Bell Test","volume":"3","author":"Lim","year":"2013","journal-title":"Phys. Rev. X"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"140501","DOI":"10.1103\/PhysRevLett.113.140501","article-title":"Fully device-independent quantum key distribution","volume":"113","author":"Vazirani","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1103\/PhysRevA.58.1827","article-title":"Optimal cloning of pure states","volume":"58","author":"Werner","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0375-9601(00)00441-2","article-title":"A quantum approach to static games of complete information","volume":"272","author":"Marinatto","year":"2000","journal-title":"Phys. Lett. A"},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"145303","DOI":"10.1088\/1751-8113\/43\/14\/145303","article-title":"Uniqueness of Nash equilibria in a quantum Cournot duopoly game","volume":"43","author":"Sekiguchi","year":"2010","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_25","first-page":"538","article-title":"Recasting Mermin\u2019s multi-player game into the framework of pseudo-telepathy","volume":"5","author":"Brassard","year":"2005","journal-title":"Quantum Inf. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1103\/PhysRevLett.82.1052","article-title":"Quantum strategies","volume":"82","author":"Meyer","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1038\/s41534-017-0021-7","article-title":"Quantum gambling based on Nash equilibrium","volume":"3","author":"Zhang","year":"2017","journal-title":"NPJ Quantum Inf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"230404","DOI":"10.1103\/PhysRevLett.104.230404","article-title":"Guess your neighbors input: A multipartite nonlocal game with no quantum advantage","volume":"104","author":"Almeida","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","unstructured":"Fudenberg, D., and Tirole, J. (1995). Game Theory, MIT Press."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1145\/1461928.1461951","article-title":"The complexity of computing a Nash equilibrium","volume":"52","author":"Daskalakis","year":"2009","journal-title":"Commun. 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