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Quantum horse racing game

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Abstract

In this research, we investigate the horse racing game, a two-player game with six strategies. Our objective is to develop a theoretical framework for the game by employing the process of quantization. The Nash equilibrium (NE) of the quantum horse racing game is analyzed through an examination of the payoff matrix, and the results are compared to those of the classical horse racing game. Our findings demonstrate that the quantum horse racing game features both pure and mixed strategy NE, whereas the classical horse racing game possesses only mixed strategy NE. Additionally, our results indicate that the quantum horse racing game can mitigate the risks associated with the zero-sum game while outperforming the classical game.

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References

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. Du, J.F., Li, H., Xu, X.D., et al.: Experimental realization of quantum games on a quantum computer. Phys. Rev. Lett. 88, 137902 (2002)

    Article  ADS  Google Scholar 

  5. Jing, L., Zhou, L., Kuang, L.M.: Linear optics implementation for quantum game with two players. Phys. Lett. A 330, 48–53 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  6. Zhou, L., Kuang, L.M.: Proposal for optically realizing quantum game. Phys. Lett. A 315, 426–430 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  7. Muhammad, S., Tavakoli, A., et al.: Quantum bidding in bridge. Phys. Rev. 4, 021047 (2014)

    Article  Google Scholar 

  8. Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301(R) (2001)

    Article  ADS  Google Scholar 

  9. Iqbal, A., Toor, A.H.: Quantum mechanics gives stability to nash equilibrium. Phys. Rev. A 65, 022306 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  10. Brassard, G., Broadbent, A., Tapp, A.: Quantum pseudo-telepathy. Foundation Phys 35, 1877–1907 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  11. Oliveira, D.S., Sousa, P.B.M., Ramos, R. V.: Quantum search algorithm using quantum bit string comparator, International Telecommunications Symposium, Fortaleza, Brazil, 582–585 (2006).

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

    Article  ADS  MathSciNet  Google Scholar 

  13. Khan, S., Ramzan, M., Khan, M.K.: Quantum model of bertrand duopoly. Chin. Phys. Lett. 27, 080302 (2010)

    Article  ADS  Google Scholar 

  14. FraCkiewicz, P., Sladkowski, J.: Quantum approach to bertrand duopoly. Q. Inf. Proc 15, 3637–3650 (2016)

    Article  MathSciNet  Google Scholar 

  15. Khan, F.S., Solmeyer, N., Balu, R., Humble, T.S.: Quantum games: A review of the history, current state and interpretation. Q. Inf. Proc 17, 309 (2018)

    Article  MathSciNet  Google Scholar 

  16. Agarwal, G.S., Puri, R.R., Singh, R.P.: Atomic Schro Èdinger cat states. Phys. Rev. A 56(3), 2249 (1997)

    Article  ADS  Google Scholar 

  17. Henderson, L., Vedral, L.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34, 6899 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  18. Consuelo-Leal, A., Araujo-Ferreira, A.G., Vidoto, E.L.G., Lucas-Oliveira, E., Bonagamba, T.J., Auccaise, R.: NMR Hamiltonian as an effective Hamiltonian to generate Schrödinger’s cat states. Q. Inf. Proc 21, 265 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

This project was supported by funding from the Natural Science Foundation of Zhejiang Province (Grant No. LY19A050004).

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  1. Department of Mathematics, Faculty of Science, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Ji Chen

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  1. Ji Chen
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Correspondence to Ji Chen.

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Chen, J. Quantum horse racing game. Quantum Inf Process 23, 186 (2024). https://doi.org/10.1007/s11128-024-04401-1

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