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arXiv:1801.02053 · Lecture notes in computer science

Nash Embedding and Equilibrium in Pure Quantum States

Faisal Shah Khan, Travis S. Humble

Published Jan 1, 2019• 12 citations
arXivHTMLPDF
DOI
10.1007/978-3-030-14082-3_5

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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.