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Characterizing the Nash equilibria of a three-player Bayesian quantum game

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Abstract

Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner’s dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD game is set up with two types of the second prisoner and the first prisoner plays with them with probability p and \(1-p\), respectively. The Bayesian nature of the game manifests in the uncertainty that the first prisoner faces about his opponent’s type which is encoded either in a classical probability or in the amplitudes of a wave function. Here, we consider scenarios with asymmetric payoffs between the first and second prisoner for different values of the probability, p, and the entanglement. Our results indicate a class of Nash equilibria (NE) with rich structures, characterized by a phase relationship on the strategies of the players. The rich structure can be exploited by the referee to set up rules of the game to push the players toward a specific class of NE. These results provide a deeper insight into the quantum advantages of Bayesian games over their classical counterpart.

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Authors and Affiliations

  1. Sensors and Electron Devices Directorate, Army Research Laboratory, Adelphi, MD, 20783, USA

    Neal Solmeyer

  2. Mississippi Valley State University, 14000 Highway 82 West, Itta Bena, MS, 38941, USA

    Ricky Dixon

  3. Computer and Information Sciences Directorate, Army Research Laboratory, Adelphi, MD, 20783, USA

    Radhakrishnan Balu

Authors
  1. Neal Solmeyer
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  2. Ricky Dixon
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  3. Radhakrishnan Balu
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Correspondence to Neal Solmeyer.

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Solmeyer, N., Dixon, R. & Balu, R. Characterizing the Nash equilibria of a three-player Bayesian quantum game. Quantum Inf Process 16, 146 (2017). https://doi.org/10.1007/s11128-017-1593-z

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  • DOI: https://doi.org/10.1007/s11128-017-1593-z

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