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Quantum approach to Bertrand duopoly

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Abstract

The aim of the paper is to study the Bertrand duopoly example in the quantum domain. We use two ways to write the game in terms of quantum theory. The first one adapts the Li–Du–Massar scheme for the Cournot duopoly. The second one is a simplified model that exploits a two qubit entangled state. In both cases, we focus on finding Nash equilibria in the resulting games. Our analysis allows us to take another look at the classic model of Bertrand.

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Notes

  1. We should stress here that quantum games are games in the standard sense and the reader should not assign any mysterious contexts to the adjective quantum.

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Acknowledgments

We would like to thank the Reviewers for discussion which undoubtedly improved the quality of our work. Work by Piotr Fra̧ckiewicz was supported by the Ministry of Science and Higher Education under the project Iuventus Plus IP2014 010973.

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Authors and Affiliations

  1. Institute of Mathematics, Pomeranian University, ul. Arciszewskiego 22d, 76-200, Słupsk, Poland

    Piotr Fra̧ckiewicz

  2. Institute of Physics, University of Silesia, ul Uniwersytecka 4, 40-007, Katowice, Poland

    Jan Sładkowski

Authors
  1. Piotr Fra̧ckiewicz
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  2. Jan Sładkowski
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Corresponding author

Correspondence to Piotr Fra̧ckiewicz.

Additional information

This work was supported by the Ministry of Science and Higher Education in Poland under the project Iuventus Plus IP2014 010973 in the years 2015–2017.

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Fra̧ckiewicz, P., Sładkowski, J. Quantum approach to Bertrand duopoly. Quantum Inf Process 15, 3637–3650 (2016). https://doi.org/10.1007/s11128-016-1355-3

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  • DOI: https://doi.org/10.1007/s11128-016-1355-3

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