aiqbench analysis
This study demonstrates that entanglement can enforce evolutionary stability in specific quantum game formulations, but this effect vanishes when the strategy space is expanded to full SU(2) symmetry due to the emergence of payoff-neutral mutants. The findings highlight a critical dependence on restricted parameter spaces within Eisert-Wilkens-Lewenstein (EWL) quantization schemes for maintaining strict Nash equilibria in symmetric games.
Entanglement, Evolutionary Stability, and Strategy-Space Dependence in an EWL Quantum Game
arXiv:2607.21103v1 Announce Type: new 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 $s^*=(\pi/2,\pi/4)$ becomes a strict symmetric Nash equilibrium, and hence an evolutionarily stable strategy, for every $\gamma>0$. 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 $SU(2)$.
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 $s^*=(\pi/2,\pi/4)$ becomes a strict symmetric Nash equilibrium, and hence an evolutionarily stable strategy, for every $\gamma>0$. 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 $SU(2)$.
arXiv:2607.21103 [quant-ph]
(or arXiv:2607.21103v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.21103 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 192 words
