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On collective quantum games

  • Ramón Alonso-SanzEmail author
Article
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Abstract

This article studies iterative collective quantum games, where every player interacts with four partners and four mates. Four two-person game types are scrutinized by allowing the players to adopt the strategy of his best paid mate. Particular attention is paid in the study to the effect of variable degree of entanglement on Nash equilibrium strategy pairs in fair games where both players are able to update their strategies. The behaviour of unfair collective iterated games where only one of the players updates his strategies is also scrutinized.

Keywords

Collective Quantum Games 
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Notes

Acknowledgements

This work has been funded by the Spanish Grant MTM2015-63914-P. Part of the computations of this work were performed in FISWULF, an HPC machine of the International Campus of Excellence of Moncloa, funded by the UCM and Feder Funds.

References

  1. 1.
    Alonso-Sanz, R.: Collective quantum games with Werner-like states. Physica A 510, 812–827 (2018)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Alonso-Sanz, R.: Spatial correlated games. R. Soc. Open Sci. 4(11), 171361 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: On the effect of quantum noise in a quantum Prisoner’s Dilemma cellular automaton. Quantum Inf. Process. 16(6), 161 (2017)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton with probabilistic updating. J. Cell. Autom. 11(2–3), 145–166 (2016)MathSciNetGoogle Scholar
  5. 5.
    Alonso-Sanz, R.: Variable entangling in a quantum battle of the sexes cellular automaton. In: ACRI-2014. LNCS, vol. 8751, pp. 125–135 (2014)Google Scholar
  6. 6.
    Alonso-Sanz, R., Shitu, H.: A quantum Samaritan’s Dilemma cellular automaton. R. Soc. Open Sci. 4(6), 160669 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Alonso-Sanz, R., Situ, H.: On the effect of quantum noise in a quantum relativistic Prisoner’s Dilemma cellular automaton. Int. J. Theor. Phys. 55(12), 5265–5279 (2016)CrossRefGoogle Scholar
  8. 8.
    Benjamin, S.C., Hayden, P.M.: Comment on “Quantum Games and Quantum Strategies”. Phys. Rev. Lett. 87, 069801 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    Binmore, K. : Just Playing: Game Theory and the Social Contract II. MIT Press, Cambridge. ISBN 0-262-02444-6 (1998)Google Scholar
  11. 11.
    Binmore, K.: Game Theory: A Very Short Introduction. Oxford UP, Oxford (2007)CrossRefGoogle Scholar
  12. 12.
    Buchanan, J.M.: The Samaritan’s Dilemma. In: Phelps, E.S., Sage, R. (eds.) Altruism, Morality, and Economic Theory, p. 71. Russell Sage Foundation, New York City (1975)Google Scholar
  13. 13.
    Du, J.F., Xu, X.D., Li, H., Zhou, X., Han, R.: Entanglement playing a dominating role in quantum games. Phys. Lett. A 89(1–2), 9–15 (2001)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Du, J.F., Li, H., Xu, X.D., Zhou, X., Han, R.: Phase-transition-like behaviour of quantum games. J. Phys. A Math. Gen. 36(23), 6551–6562 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Eisert, J., Wilkens, M., Lewenstein, M.: Comment on “Quantum games and quantum strategies”-reply. Phys. Rev. Lett. 87, 069802 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Eisert, J., Wilkens, M.: Quantum games. J. Mod. Opt. 47(14–15), 2543–2556 (2000)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Groisman, B.: When quantum games can be played classically: in support of vanEnk-Pike’s assertion. arXiv:1802.00260 (2018)
  19. 19.
    Iqbal, A., Chappell, J.M., Abbott, D.: On the equivalence between non-factorizable mixed-strategy classical games and quantum games. R. Soc. Open Sci. 3, 150477 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Owen, G.: Game Theory. Academic Press, Cambridge (1995)zbMATHGoogle Scholar
  21. 21.
    Ozdemir, S.K., Shimamura, J., Morikoshi, F., Imoto, N.: Dynamics of a discoordination game with classical and quantum correlations. Phys. Lett. A 333, 218–231 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    Rasmussen, E.: Games and Information, An Introduction to Game Theory. Blackwell, Oxford (2001)Google Scholar
  23. 23.
    Schiff, J.L.: Cellular Automata: A Discrete View of the World. Wiley, New York (2008)zbMATHGoogle Scholar
  24. 24.
    van Enk, S.J., Pike, R.: Classical rules in quantum games. Phys. Rev. A 66(2), 024306 (2002)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Vyas, N., Benjamin, C.: Negating van Enk-Pike’s assertion on quantum games OR Is the essence of a quantum game captured completely in the original classical game? arXiv:1701.08573 (2017)

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ETSIAAB (Estadistica, GSC)Technical University of MadridMadridSpain

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