International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3550–3562 | Cite as

A Collective Quantum Matching Pennies Game

  • Ramón Alonso-Sanz


This article studies an iterative collective matching pennies (MP) quantum game, where every player interacts with his neighbours. The MP game evolves by allowing every player to adopt the strategy of his best paid mate. The behaviour in fair and unfair contests is examined.


Collective Quantum Matching pennies Games 



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.


  1. 1.
    Alonso-Sanz, R.: Spatial correlated games. Royal Soc. Open Sci. 11(17), 1361 (2017)MathSciNetGoogle Scholar
  2. 2.
    Alonso-Sanz, R.: Variable entangling a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process 14, 147–164 (2015)MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: Variable entangling in a quantum battle of the sexes cellular automaton. ACRI-2014. LNCS 8751, 125–135 (2014)Google Scholar
  4. 4.
    Benjamin, S.C., Hayden, P.: Comment on quantum games and quantum strategies. Phys. Rev. Lett. 87, 069801 (2001)CrossRefADSGoogle Scholar
  5. 5.
    Benjamin, S.C., Hayden, P.: Multiplayer quantum games. Phys. Rev. A 64, 030301 (2001)CrossRefADSGoogle Scholar
  6. 6.
    Eisert, J., Wilkens, M., Lewenstein, M.: Comment on quantum games and quantum strategies-reply. Phys. Rev. Lett. 87, 069802 (2001)CrossRefADSGoogle Scholar
  7. 7.
    Eisert, J., Wilkens, M.: Quantum games. J. Modern Opt. 47(14-15), 2543–2556 (2000)MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    Flitney, A.P., Abbott, D: Advantage of a quantum player over a classical one in 2x2 quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    Gibbons, R.: Game Theory for Applied Economists, pp 29–33. Princeton University Press, Princeton (1992)Google Scholar
  11. 11.
    Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Physical Soc. Japan 78, 014803 (2009). arXiv:0807.3599 CrossRefADSGoogle Scholar
  12. 12.
    Iqbal, A., Chappell, J.M., Abbott, D.: On the equivalence between non-factorizable mixed-strategy classical games and quantum games. Royal Soc. Open Sci. 3, 150477 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Owen, G.: Game Theory. Academic Press, Cambridge (1995)zbMATHGoogle Scholar
  14. 14.
    Schiff, J.L.: Cellular Automata: A Discrete View of the World. Wiley, New York (2008)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ETSIAAB (Estadistica, GSC) C.UniversitariaTechnical University of MadridMadridSpain

Personalised recommendations