Skip to main content
SpringerLink
Log in

Cournot and Stackelberg duopoly games in the purview of modified EWL scheme

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The recently proposed modified EWL scheme aims to understand the role of two-qubit entangling operators in controlling the game dynamics. In this work, we quantize the classical Cournot and Stackelberg duopoly games using the modified EWL scheme to understand duopoly games from the perspective of quantum operators. We have found two interesting results: Firstly, in both Cournot and Stackelberg duopoly, the profit function of the firms depends upon the entangling operator only when the firms adapt different strategies. Secondly, the outcome of the firms can be made equal with a suitable choice of entangling operator upon interchanging the strategies of the firms. We have shown the validity of both the theorems for pure and mixed strategies. The observation holds good for both Cournot and Stackelberg duopoly games. Further, we have shown the difference in the outcome of the firms in the Stackelberg duopoly game can be minimized to some extent with the help of suitable entangling operators and strategies.

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

Similar content being viewed by others

References

  1. Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Oxford (1947)

    MATH  Google Scholar 

  2. Colman, A.M.: Game Theory and its Applications in the Social and Biological Sciences. Butterworth-Heinemam, Oxford (1995)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. Guo, H., Zhang, J., Koehler, G.J.: A survey of quantum games. Decis. Support Syst. 46, 318 (2008)

    Article  Google Scholar 

  5. Flitney, A.P., Abbott, D.: An introduction to quantum game theory. Fluct. Noise Lett. 2, R175 (2002)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Khan, F.S., Solmeyer, N., Balu, R., et al.: Quantum games: a review of the history, current state, and interpretation. Quant. Inf. Process. 17, 309 (2018)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. Vijayakrishnan, V., Balakrishnan, S.: Role of two-qubit entangling operators in the modified Eisert-Wilkens-Lewenstein approach of quantization. Quantum Inf. Process. 18, 112 (2019)

    Article  ADS  Google Scholar 

  11. Vijayakrishnan, V., Balakrishnan, S.: Significance of entangling operators in the purview of modified EWL scheme. Quantum Inf. Process. 19, 315 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  12. Gibbons, R.: Game Theory for Applied Economists. Princeton University Press, Oxford (1992)

    Book  Google Scholar 

  13. Cournot, A.: Researches Into the Mathematical Principles of the Theory of Wealth, Edited by N. Bacon, Macmillan, New York (1897)

  14. Stackelberg, H.V.: Marktform und Gleichgewicht. Julius Springer, Vienna (1934)

    MATH  Google Scholar 

  15. Iqbal, A., Toor, A.H.: Backward-induction outcome in a quantum game. Phys. Rev. A 65, 052328 (2002)

    Article  ADS  Google Scholar 

  16. Lo, C.F., Kiang, D.: Quantum Stackelberg duopoly. Phys. Letts. A 318, 333–336 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  17. Li, H., Du, J., Massar, S.: Continuous-variable quantum games. Phys. Letts. A 306, 73–78 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  18. Frackiewicz, P.: Remarks on quantum duopoly schemes. Quantum Inf. Process. 15, 121–136 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. Shi, L., Xu, F., Chen, Y.: Quantum Cournot duopoly game with isoelastic demand function. Phys. A. 566, 125614 (2021)

    Article  MathSciNet  Google Scholar 

  20. Lo, C.F., Kiang, D.: Quantum Stackelberg duopoly with incomplete information. Phys. Letts. A 346, 65–70 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  21. Frackiewicz, P.: On subgame perfect equilibria in quantum Stackelberg duopoly with incomplete information. Phys. Letts. A 382, 3463–3469 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. Frackiewicz, P.: Quantum approach to Cournot-type Competition. Int. J. Theor. Phys. 57, 353–362 (2018)

    Article  MathSciNet  Google Scholar 

  23. Shi, L., Xu, F.: Quantum Stackelberg duopoly game with isoelastic demand function. Phys. Letts. A 385, 126956 (2021)

    Article  MathSciNet  Google Scholar 

  24. Zhang, J., Vala, J., Whaley, K.B., Sastry, S.: Geometric theory of nonlocal two-qubit operations. Phys. Rev. A 67, 042313 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  25. Rezakhani, A.T.: Characterization of two-qubit perfect entanglers. Phys. Rev. A 70, 052313 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  26. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  27. Elgazzar, A.S.: Quantum prisoner’s dilemma in a restricted one parametric strategic space. Appl. Math. Comput. 370, 124927 (2020)

    MathSciNet  MATH  Google Scholar 

  28. Elgazzar, A.S.: Coopetition in quantum prisoner’s dilemma and COVID-19. Quant. Info. Process. 20, 102 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  29. Elgazzar, A.S., Elrayes, H.A.: Quantum symmetric cooperative game with a harmonious coalition. Zeitschrift für Naturforschung A 73(1), 69–73 (2018)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu, Vellore, 632014, India

    A. V. S. kameshwari & S. Balakrishnan

Authors
  1. A. V. S. kameshwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Balakrishnan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

kameshwari, A.V.S., Balakrishnan, S. Cournot and Stackelberg duopoly games in the purview of modified EWL scheme. Quantum Inf Process 20, 337 (2021). https://doi.org/10.1007/s11128-021-03281-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03281-z

Keywords

Search

Navigation