Prisoners' Dilemma in Presence of Collective Dephasing

Abstract

We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $\gamma$. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it bifurcates into two new Nash equilibria $Q\otimes D$ and $D\otimes Q$. Furthermore for maximum value of decoherence \ $C\otimes D$ and $D\otimes C$ also become Nash equilibria. At this stage the game has four Nash equilibria. On the other hand for three parameters set of strategies there is no pure strategy Nash equilibrium however there is mixed strategy (non unique) Nash equilibrium that is not affected by collective dephasing..

11 pages

References in corpus (2)

• Efficient quantum key distribution over a collective noise channel
• Quantum Games with Correlated Noise

Cited by in corpus (5)

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• Note on maximally entangled Eisert-Lewenstein-Wilkens quantum games
• Quantum Cournot model based on general entanglement operator