AI 中文总结
研究EWL量子化对对称2×2博弈进化稳定性的影响，在受限双参数EWL策略空间中量子均衡是进化稳定策略，扩展到完整三参数SU(2)族时，虽保留纳什均衡但出现问题，表明纠缠仅在受限EWL策略空间稳定均衡。
AI 中文摘要
我们研究了Eisert-Wilkens-Lewenstein（EWL）量子化如何影响对称2×2博弈中的进化稳定性，该博弈的内部混合纳什均衡不是进化稳定的。在受限的双参数EWL策略空间中，对于每个γ>0，量子均衡s* =（π/2，π/4）成为严格对称纳什均衡，从而是进化稳定策略。将可允许纯策略扩展到完整的三参数SU(2)族保留了纳什均衡，但引入了连续的收益中性突变体，导致严格性和第二个ESS条件不成立。因此，纠缠仅在受限的EWL策略空间内稳定均衡；这种效应在扩展到完整的SU(2)时不存在。
英文摘要
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 $SU(2)$.
Comments11 pages, 2 figures
