Evolutionary stability and payoff equivalence in an Eisert-Wilkens-Lewenstein quantum game
Abstract
An evolutionarily stable strategy (ESS) is a strategy that, once adopted by a population, cannot be invaded by any sufficiently rare alternative (mutant) strategy. We analyse evolutionary stability in an Eisert--Wilkens--Lewenstein (EWL) quantization of a symmetric 2×2 coordination game, whose classical mixed equilibrium p*=1/2 is not an ESS. In the restricted two-parameter EWL strategy space, the corresponding quantum strategy is a strict symmetric Nash equilibrium and an ESS for every entanglement strength γ>0. In the full SU(2) strategy space it remains a Nash equilibrium, but in the unreduced game, in which every unitary is a distinct strategy, exact payoff duplicates preclude strictness and ESS for every pure strategy. For the agreement-payoff class, the payoff factors through a Bloch map; identifying payoff-equivalent unitaries gives the reduced space U(1)backslash SU(2)≅ S2, where strictness and ESS are restored for γ>0. An arbitrarily small perturbation outside this class that preserves p*=1/2 yields a profitable deviation, so the reduced-space result is not generic.
Versions
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BibTeX
@misc{iqbal2026evolutionary,
title = {{Evolutionary stability and payoff equivalence in an Eisert-Wilkens-Lewenstein quantum game}},
author = {Azhar Iqbal and Derek Abbott},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.21103},
eprint = {2607.21103},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21103},
}
RIS
TY - UNPB
TI - Evolutionary stability and payoff equivalence in an Eisert-Wilkens-Lewenstein quantum game
AU - Azhar Iqbal
AU - Derek Abbott
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.21103
UR - https://arxiv.org/abs/2607.21103
AB - An evolutionarily stable strategy (ESS) is a strategy that, once adopted by a population, cannot be invaded by any sufficiently rare alternative (mutant) strategy. We analyse evolutionary stability in an Eisert--Wilkens--Lewenstein (EWL) quantization of a symmetric 2×2 coordination game, whose classical mixed equilibrium p^*=1/2 is not an ESS. In the restricted two-parameter EWL strategy space, the corresponding quantum strategy is a strict symmetric Nash equilibrium and an ESS for every entanglement strength γ>0. In the full SU(2) strategy space it remains a Nash equilibrium, but in the unreduced game, in which every unitary is a distinct strategy, exact payoff duplicates preclude strictness and ESS for every pure strategy. For the agreement-payoff class, the payoff factors through a Bloch map; identifying payoff-equivalent unitaries gives the reduced space U(1)backslash SU(2)≅ S^2, where strictness and ESS are restored for γ>0. An arbitrarily small perturbation outside this class that preserves p^*=1/2 yields a profitable deviation, so the reduced-space result is not generic.
ER -