The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

Shubhayan Sarkar, Colin Benjamin

Salman Khan, Sher Alam

Faisal Shah Khan, Travis S. Humble

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. We show here that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

Faisal Shah Khan, Travis S. Humble

J Du, Ruitian Han, H Li +2 more

We investigate Nash Equilibrium in quantum games by quantizing the Battle of Sexes Game, finding that there is no unique but infinite Nash Equilibrium in it. A method is also provided to check that whether a quantum game has unique Nash Equilibrium, which could be helpful for multi-player quantum games.

Philip V. Fellman, Jonathan Vos Post