Quantum Nash Equilibrium

Classical game theory has long provided a framework to model strategic decision- making among rational agents. Yet, when this framework is extended into the quantum regime, new equilibria emerge that challenge classical intuitions about co- operation and defection. In this work, we examine the quantum version of the Pris- oner’s Dilemma using the Eisert–Wilkens–Lewenstein (EWL) quantization model. We present a detailed derivation of the quantum Nash equilibrium for the max- imally entangled case (γ= π/2), demonstrating that the quantum strategy pair Q⊗Qyields a Pareto-superior outcome compared to the classical Nash equilibrium of mutual defection. By comparing payoff structures, unitary strategy operators, and entanglement effects, we show how quantum correlations fundamentally alter the structure of rational choice.