2026/07/23 by Azhar Iqbal, Derek Abbott
#quant-ph
We examine how Eisert--Wilkens--Lewenstein (EWL) quantization affects evolutionary stability in a symmetric 2×2 game whose interior mixed Nash equilibrium is not evolutionarily stable. In the restricted two-parameter EWL strategy space, the quantum equilibrium s^*=(π/2,π/4) becomes a strict symmetric Nash equilibrium, and hence an evolutionarily stable strategy, for every γ>0. Extending the admissible pure strategies to the full three-parameter SU(2) family preserves the Nash equilibrium but introduces a continuum of payoff-neutral mutants, causing strictness and the second ESS condition to fail. Thus, entanglement stabilizes the equilibrium only within the restricted EWL strategy space; the effect does not survive enlargement to full SU(2).