Prisoners' Dilemma in Presence of Collective Dephasing

TL;DR

This paper studies the quantum Prisoner's Dilemma under collective dephasing, revealing how decoherence affects the stability and number of Nash equilibria in the game.

Contribution

It introduces a quantum version of the Prisoner's Dilemma with collective dephasing and analyzes how decoherence influences Nash equilibria.

Findings

Q⊗Q is Nash equilibrium below a critical dephasing time

New Nash equilibria emerge beyond the critical dephasing time

A non-unique mixed strategy Nash equilibrium exists unaffected by 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..