Nash embedding and equilibrium in pure quantum states

TL;DR

This paper demonstrates that Nash equilibrium stability can be achieved for pure quantum strategies using the Nash embedding theorem, extending the concept beyond mixed strategies in quantum game theory.

Contribution

It introduces a novel application of the Nash embedding theorem to ensure fixed-point stability for pure quantum strategies in game theory.

Findings

Nash equilibrium stability extends to pure quantum strategies.

Application of Nash embedding theorem in quantum game theory.

Players can optimize pure quantum states under constraints.

Abstract

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. In this letter, we show 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.