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Quantum Bayesian game with symmetric and asymmetric information

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Abstract

We use one of the influential quantum game models, the Marinatto–Weber model, to investigate quantum Bayesian game. We show that in a quantum Bayesian game which has more than one Nash equilibrium, one equilibrium stands out as the compelling solution, whereas two Nash equilibria seem equally compelling in the classical Bayesian game.

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Notes

  1. There exist two mixed strategy Nash equilibria in this game, but their payoffs are smaller than \((B',B',B',B')\)’s and \((S',S',S',S')\)’s (see “Appendix” for the payoffs), thus rational players would not prefer mixed strategy Nash equilibria.

  2. Any mixed strategy Nash equilibrium’s payoff is smaller than \((1,1,1,1)\)’s payoff because \((1,1,1,1)\) has the highest payoff among the pure strategy profiles (see “Appendix” for the payoffs), thus rational players would not prefer mixed strategy Nash equilibria.

  3. There exists one mixed strategy Nash equilibrium in this game, but its payoffs are smaller than \((B',B',B')\)’s (see “Appendix” for the payoffs), thus rational players would not prefer the mixed strategy Nash equilibrium.

  4. Any mixed strategy Nash equilibrium’s payoff is smaller than \((1,1,1)\)’s payoff because \((1,1,1)\) has the highest payoff among the pure strategy profiles (see “Appendix” for the payoffs), thus rational players would not prefer mixed strategy Nash equilibria.

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Acknowledgments

We are very grateful to Professor Weinstein, Editor-in-Chief, and the anonymous reviewers for their invaluable comments and detailed suggestions that helped to improve the quality of this paper. This work is supported by the Natural Science Foundation of Guangdong Province of China (Grant Nos. 2014A030310265, 2014A030313157) and the National Natural Science Foundation of China (Grant No. 61472452).

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Haozhen Situ

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Correspondence to Haozhen Situ.

Appendix

Appendix

The appendix contains four tables. Table 1 lists the pure and mixed strategy Nash equilibria in the classical Bayesian game with symmetric information, which appears in Sect. 2. Table 2 lists the payoffs of the pure strategy profiles in the quantum Bayesian game with symmetric information, which appears in Sect. 4. Table 3 lists the pure and mixed strategy Nash equilibria in the classical Bayesian game with asymmetric information, which appears in Sect. 5. Table 4 lists the payoffs of the pure strategy profiles in the quantum Bayesian game with asymmetric information, which appears in Sect. 5.

Table 1 Classical Bayesian game with symmetric information
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Table 2 Quantum Bayesian game with symmetric information
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Table 3 Classical Bayesian game with asymmetric information
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Table 4 Quantum Bayesian game with asymmetric information
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Situ, H. Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf Process 14, 1827–1840 (2015). https://doi.org/10.1007/s11128-015-0984-2

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