Skip to main content
SpringerLink
Log in

A cellular automaton implementation of a quantum battle of the sexes game with imperfect information

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The dynamics of a spatial quantum formulation of the iterated battle of the sexes game with imperfect information is studied in this work. The game is played with variable entangling in a cellular automata manner, i.e. with local and synchronous interaction. The effect of spatial structure is assessed in fair and unfair scenarios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 14(1), 147–164 (2015)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)

    Article  MathSciNet  ADS  Google Scholar 

  3. Alonso-Sanz, R.: Variable entangling in a quantum battle of the sexes cellular automaton. LNCS 8751, pp. 125–135 (2014)

  4. Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Inf. Process. 12(5), 1835–1850 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  6. Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific Pub, Singapore (2011)

    MATH  Google Scholar 

  7. Benjamin, S.C., Hayden, P.M.: Comment on “Quantum games and quantum strategies”. Phys. Rev. Lett. 87(6), 069801 (2001)

    Article  ADS  Google Scholar 

  8. Bleiler, S.: A formalism for quantum games and an application. http://arxiv.org/abs/0808.1389 (2008)

  9. Branderburger, A.: The relationship between quantum and classical correlation games. Games Econ. Behav. 89, 157–183 (2010)

    MathSciNet  Google Scholar 

  10. Cheon, T., Iqbal, A.: Bayesian Nash equilibria and bell inequalities. J. Phys. Soc. Jpn. 77(2), 024801 (2008). doi:10.1143/JPSJ.77.024801

  11. Du, J., Ju, C., Li, H.: Quantum entanglement helps in improving economic efficiency. J. Phys. A Maths. Gen. 38, 1559–1565 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Du, J.F., Xu, X.D., Li, H., Zhou, X., Han, R., et al.: Entanglement playing a dominating role in quantum games. Phys. Lett. A 89(1–2), 9–15 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. 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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Flitney, A.P., Abbott, D.: Advantage of a quantum player over a classical one in \(2\times 2\) quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Flitney. A.P., Abbott, D.: An Introduction to quantum game theory. Fluct. Noise Lett. 02, R175. http://arxiv.org/pdf/quant-ph/0208069 (2002)

  17. Frackiewicz, P.: A new quantum scheme for normal-form games. Process. Quantum Inf. (2015). doi:10.1007/s11128-015-0979-z

  18. Iqbal, A., Chappell, J.M., Li, Q., Pearce, C.E.M., Abbott, D.: A probabilistic approach to quantum Bayesian games of incomplete information. Quantum Inf. Process. 13(12), 2783–2800 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Khan, F.S.: Dominant Strategies in Two Qubit Quantum Computations. http://arxiv.org/abs/1410.0940 (2014)

  20. Khan, F.S., Phoenix, S.J.D.: Mini-maximizing two qubit quantum computations. Quantum Inf. Process. 12(12), 3807–3819 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Khan, F.S., Phoenix, S.J.D.: Gaming the quantum. Quantum Inf. Comput. 13(3–4), 231–244 (2013)

    MathSciNet  Google Scholar 

  22. Landsburg, S.E.: Quantum game theory. To appear in the The Wiley Encyclopedia of Operations Research and Management Science. http://arxiv.org/pdf/1110.6237v1 (2011)

  23. Landsburg, S.E.: Quantum game theory. Notices of the AMS. http://www.ams.org/notices/200404/fea-landsburg (2004)

  24. Levine, D.K.: Quantum games have no news for economists. http://levine.sscnet.ucla.edu/papers/quantumnonews (2005)

  25. Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Lett. A 272, 291–303 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Miszczak, J.A., Pawela, L., Sladkowski, J.: General model for an entanglement-enhanced composed quantum game on a two-dimensional lattice. Fluct. Noise Lett. 13(2) 1450012 (2014) http://arxiv.org/abs/1306.4506

  28. Nawaz, A., Toor, A.H.: Dilemma and quantum battle of sexes. J. Phys. A Math. Gen. 37(15), 4437 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A Math. Gen. 37(47), 11457 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)

    MATH  Google Scholar 

  31. Owen, G.: Game Theory. Academic Press, New York (1995)

    MATH  Google Scholar 

  32. Pappa, A., Kumar, N., Lawson, T., Santha, M., Zhang, S., Diamanti, E., Kerenidis, I.: Nonlocality and conflicting interest games. Phys. Rev. Lett. 114, 020401 (2015)

    Article  ADS  Google Scholar 

  33. Phoenix, S.J.D., Khan, F.S.: The role of correlations in classical and quantum games. Fluct. Noise Lett. 12(3), 1350011 (2013)

    Article  Google Scholar 

  34. Piotrowski, E.W., Sladkowski, J.: An invitation to quantum game theory. Int. J. Theor. Phys. 42(5), 1089–1099 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Situ, H.: A quantum approach to play asymmetric coordination games. Quantum Inf. Process. 13(3), 591–599 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. Situ, H.: Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf. Process. 14(6), 1827–1840 (2015)

  37. Wiesner, K.: Quantum cellular automata. Encycl. Complex. Syst. Sci. 7154–7164. http://arxiv.org/abs/0808.0679 (2009)

Download references

Acknowledgments

This work was supported by the Spanish Grant M2012-39101-C02-01. Part of the computations were performed in the HPC machines EOLO and FISWULF, based on the International Campus of Excellence of Moncloa, funded by the Spanish Government and Feder funds.

Author information

Authors and Affiliations

  1. Technical University of Madrid, ETSIA (Estadística, GSC). C. Universitaria, 28040, Madrid, Spain

    Ramón Alonso-Sanz

Authors
  1. Ramón Alonso-Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramón Alonso-Sanz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alonso-Sanz, R. A cellular automaton implementation of a quantum battle of the sexes game with imperfect information. Quantum Inf Process 14, 3639–3659 (2015). https://doi.org/10.1007/s11128-015-1080-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1080-3

Keywords

Search

Navigation