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Theory of quantum games and quantum economic behavior

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Abstract

The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature. A study of quantum economic behavior will become the center of attention of economists in the coming decades. We analyze a quantum economy in which players produce and consume quantum goods. They meet randomly and barter with neighbors bilaterally for quantum goods they produced. We clarify the conditions where certain quantum goods emerge endogenously as media of exchange, called quantum commodity money. As quantum strategies are entangled, we find distinctive aspects of quantum games that cannot be explained by conventional classical games. In some situations a quantum player can acquire a quantum good from people regardless of their strategies, while on the other hand people can find quantum strategies that improve their welfare based on an agreement. Those novel properties imply that quantum games also shed new light on theories of mechanism design, auction and contract in the quantum era.

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Notes

  1. Here we identify \(\left| \psi \right\rangle \left\langle \psi \right| \) with \(\left| \psi \right\rangle \).

  2. In [42], the steady state of speculative equilibrium is characterized by \((p_{12},p_{23},p_{31})=\left( \frac{\sqrt{2}}{2},\sqrt{2}-1,1\right) =(0.707\cdots ,0.414\cdots ,1)\). In our setup, they are \((p_{12},p_{23},p_{31})=\left( \frac{5}{7},\frac{3}{7},1\right) =(0.714,0.428,1)\).

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Acknowledgements

We thank Avi Beracha for carefully reading the manuscript. This work was supported by PIMS Postdoctoral Fellowship Award (K.I.).

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  1. Department of Mathematics and Statistics and Centre for Quantum Topology and Its Applications (quanTA), University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E6, Canada

    Kazuki Ikeda

  2. Department of Physics, Osaka University, Toyonaka, Osaka, 5600043, Japan

    Shoto Aoki

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  1. Kazuki Ikeda
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K.I. designed and performed the research, interpreted the results, and wrote the paper. S.A. helped with the calculations.

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Ikeda, K., Aoki, S. Theory of quantum games and quantum economic behavior. Quantum Inf Process 21, 27 (2022). https://doi.org/10.1007/s11128-021-03378-5

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