Entanglement, Evolutionary Stability, and Strategy-Space Dependence in an EWL Quantum Game

• URL: http://arxiv.org/abs/2607.21103v1
• Date: Thu, 23 Jul 2026 09:32:21 GMT
• Title: Entanglement, Evolutionary Stability, and Strategy-Space Dependence in an EWL Quantum Game
• Abstract summary: quantization affects evolutionary stability in a symmetric $2times2$ game.<n>We show that entanglement stabilizes the equilibrium only within the restricted EWL strategy space.
• Score: 1.901453512012934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine how Eisert--Wilkens--Lewenstein (EWL) quantization affects evolutionary stability in a symmetric $2\times2$ 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 $SU(2)$.

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