Quantum two-players games, Entanglement and Nash equilibria

Abstract

The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple geometric properties of "chiral" group $SU(N)\times SU(N)$ and is based on considering the stability subgroup of the initial state of the game. The explicit forms of neither the gate operator nor the payoff matrix are necessary.

8 pages, no figures, two references added

References in corpus (3)

• Studies in the Theory of Quantum Games
• Some Topics in Quantum Games
• Werner-like States and Strategic Form of Quantum Games

Cited by in corpus (3)

• General quantum two-players games, their gate operators and Nash equilibria
• Entanglers in 3-strategies ELW games
• Gate operators for N-strategies quantum game