Resolving game theoretical dilemmas with quantum states

• URL: http://arxiv.org/abs/2304.03605v2
• Date: Thu, 2 Nov 2023 07:04:59 GMT
• Title: Resolving game theoretical dilemmas with quantum states
• Authors: Azhar Iqbal, James M. Chappell, Claudia Szabo, Derek Abbott
• Abstract summary: We present a new framework for creating a quantum version of a classical game. Using Fine's theorem, we re-express both the player payoffs and their strategies in terms of a set of marginals. We then consider particular quantum states that can potentially resolve dilemmas inherent in classical games.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new framework for creating a quantum version of a classical game, based on Fine's theorem. This theorem shows that for a given set of marginals, a system of Bell's inequalities constitutes both necessary and sufficient conditions for the existence of the corresponding joint probability distribution. Using Fine's theorem, we re-express both the player payoffs and their strategies in terms of a set of marginals, thus paving the way for the consideration of sets of marginals -- corresponding to entangled quantum states -- for which no corresponding joint probability distribution may exist. By harnessing quantum states and employing Positive Operator-Valued Measures (POVMs), we then consider particular quantum states that can potentially resolve dilemmas inherent in classical games.

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