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To move first or not to move first?

  • C. F. LoEmail author
  • D. Kiang
Article
  • 24 Downloads

Abstract

We have investigated the quantization of the multi-player Stackelberg game by proposing an asymmetric quantum entanglement operation. Due to the informational asymmetry between the leaders and followers in the Stackelberg model, it is more natural to have differential quantum entanglement in a multi-player quantum Stackelberg game. It is found that the profit functions considered in the multi-player Stackelberg model display interesting and intriguing patterns as functions of quantum entanglement parameters. In particular, differential quantum entanglement could cause the leaders to lose the first-mover advantage inherent in the classical Stackelberg model. This surprising feature raises an important question: “To move first or not to move first?”

Keywords

Quantum games Quantum entanglement Quantum strategies Stackelberg oligopoly 

Notes

References

  1. 1.
    Bierman, H.S., Fernandez, L.: Game Theory with Economic Applications, 2nd edn. Addison-Wesley, Boston (1998) Google Scholar
  2. 2.
    Gravelle, H., Rees, R.: Macroeconomics, 2nd edn. Longman, London (1992)Google Scholar
  3. 3.
    Romp, G.: Game Theory: Introduction and Applications. Oxford University Press, New York (1997)Google Scholar
  4. 4.
    Khan, F.S., Solmeyer, N., Balu, R., Humble, T.S.: Quantum games: a review of the history, current state, and interpretation. Quantum Inf. Process. 17, 309 (2018)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Alonso-Sanz, R.: Quantum Game Simulation. Springer, Basel (2019)CrossRefGoogle Scholar
  6. 6.
    Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077 (1999)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64(3), 030301 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Li, H., Du, J., Massar, S.: Continuous-variable quantum games. Phys. Lett. A 306, 73 (2002)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Lo, C.F., Kiang, D.: Quantum oligopoly. Europhys. Lett. 64(5), 592 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    Lo, C.F., Liu, K.L.: Multimode bosonic realization of the \(su\left(1,1\right) \) Lie algebra. Phys. Rev. A 48(4), 3362 (1993)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Lo, C.F., Sollie, R.: Generalized multimode squeezed states. Phys. Rev. A 47(1), 733 (1993)ADSCrossRefGoogle Scholar
  13. 13.
    Zhou, J., Ma, L., Li, Y.: Multiplayer quantum games with continuous-variable strategies. Phys. Lett. A 339, 10 (2005)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Lo, C.F., Kiang, D.: Quantum stackelberg duopoly. Phys. Lett. A 318, 333 (2003)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Iqbal, A., Toor, A.H.: Backwards-induction outcome in a quantum game. Phys. Rev. A 65, 052328 (2002)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Physics, Institute of Theoretical PhysicsThe Chinese University of Hong KongShatinHong Kong SAR

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