This note revisits Sakagami in [1] and studies whether quantum 2 × 2 games with full SU (2) strategy space admit Nash equilibria whose payoff curves do not intersect the classical (no entanglement) payoffs. By allowing duplicate payoffs in each player’s table, we construct an example that yields such “special” equilibria for any entanglement and describe a further equilibrium when there is no entanglement. We also relate the example to strong isomorphism results by Frackiewicz in [2].
References
[1]
Sakagami, Y. (2024) Characterization of Nash Equilibria for Quantum Games in General Position, with Full SU(2) Strategy Space and Varying Entanglement. QuantumInformationProcessing, 23, Article No. 395. https://doi.org/10.1007/s11128-024-04600-w
[2]
Frąckiewicz, P. (2016) Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games. AdvancesinMathematicalPhysics, 2016, Article ID: 4180864. https://doi.org/10.1155/2016/4180864
Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. PhysicalReviewLetters, 83, 3077-3080. https://doi.org/10.1103/physrevlett.83.3077
[5]
Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X., et al. (2002) Experimental Realization of Quantum Games on a Quantum Computer. PhysicalReviewLetters, 88, Article ID: 137902. https://doi.org/10.1103/physrevlett.88.137902
[6]
Du, J., Li, H., Xu, X., Zhou, X. and Han, R. (2003) Phase-Transition-Like Behaviour of Quantum Games. JournalofPhysicsA: MathematicalandGeneral, 36, 6551-6562. https://doi.org/10.1088/0305-4470/36/23/318
[7]
Rosero, A.F.H. (2004) Classification of Quantum Symmetric Nonzero-Sum 2X2 Games in the Eisert Scheme.
[8]
Flitney, A.P. (2005) Aspects of Quantum Game Theory.
[9]
Flitney, A.P. and Hollenberg, L.C.L. (2007) Nash Equilibria in Quantum Games with Generalized Two-Parameter Strategies. PhysicsLettersA, 363, 381-388. https://doi.org/10.1016/j.physleta.2006.11.044
[10]
Solmeyer, N., Dixon, R. and Balu, R. (2017) Characterizing the Nash Equilibria of a Three-Player Bayesian Quantum Game. QuantumInformationProcessing, 16, Article No. 146. https://doi.org/10.1007/s11128-017-1593-z
[11]
Solmeyer, N. and Balu, R. (2017) Characterizing the Nash Equilibria of Three-Player Bayesian Quantum Games. SPIEProceedings, Vol. 10212, 102120T. https://doi.org/10.1117/12.2262518
