Nash equilibria in quantum games with generalized two-parameter strategies

In the Eisert protocol for 2×22×2 quantum games [J. Eisert, et al., Phys. Rev. Lett. 83 (1999) 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.