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| Analysis of Nash Equilibrium of Quantum Prisoner's Dilemma with Collective-dephasing Noise Channel |
| MA Sijia, ZHANG Shuning, WANG Yihan, ZHANG Xinli
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| School of Mathematics, Liaoning Normal University, Dalian 116029, China |
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Abstract To discuss the Nash equilibrium strategy of the quantum prisoner's dilemma model under the influence of collective-dephasing noise channel, will collective-dephasing noise is introduced into the quantum game back, by MW quantization scheme to quantization of the prisoner's dilemma game, and a prisoner’s dilemma game under the effect of collective-dephasing noise is constructed. It is found that under the condition of the maximally entangle, each player’s payoff function shows periodicity about the parameter of the noise. And in the same period, along with the increase of the noise parameter, there is the unique pure quantum Nash equilibrium, two different pure quantum Nash equilibriums, and no pure quantum Nash equilibrium in different intervals. In the two noise intervals without a pure quantum Nash equilibrium, players were caught in a rock-paper-scissors loop. It shows that under the influence of collective-dephasing noise channel, players can reach Nash equilibrium when the noise parameters are in a specific interval.
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Received: 24 October 2021
Published: 21 July 2023
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