Resolving game theoretical dilemmas with quantum states

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 reexpress 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.