A Note on Special Nash Equilibria of Quantum Games

This note revisits Sakagami in [1] and studies whether quantum 2 × 2 games with full SU (2) strategy space admit Nash equilibria whose payoff curves do not intersect the classical (no entanglement) payoffs. By allowing duplicate payoffs in each player’s table, we construct an example that yields such “special” equilibria for any entanglement and describe a further equilibrium when there is no entanglement. We also relate the example to strong isomorphism results by Frackiewicz in [2].