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Nash equilibria in quantum games with generalized two-parameter strategies

Adrian P. Flitney·Lloyd C. L. Hollenberg
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Abstract

In the Eisert protocol for 2 X 2 quantum games [Phys. Rev. Lett. 83, 3077], a number of authors have investigated the features arising from making the strategic space a two-parameter subset of single qubit unitary operators. We argue that the new Nash equilibria and the classical-quantum transitions that occur are simply an artifact of the particular strategy space chosen. By choosing a different, but equally plausible, two-parameter strategic space we show that different Nash equilibria with different classical-quantum transitions can arise. We generalize the two-parameter strategies and also consider these strategies in a multiplayer setting.

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Adrian P. Flitney, Lloyd C. L. Hollenberg. 2006-10-11. Nash equilibria in quantum games with generalized two-parameter strategies. https://doi.org/10.1016/j.physleta.2006.11.044

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