A game theoretical perspective on the quantum probabilities associated with a GHZ state

TL;DR

This paper introduces a novel perspective on quantum games by modeling players' moves as directional choices in a tripartite EPR experiment, linking quantum probabilities to classical game payoffs.

Contribution

It presents a new approach to quantum games by connecting players' strategies with quantum probabilities from EPR experiments, contrasting with traditional unitary-based methods.

Findings

Defines players' moves as directional choices in EPR experiments

Expresses payoffs in terms of quantum probabilities and directional choices

Bridges classical game theory with quantum probability distributions

Abstract

In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein-Podolsky-Rosen (EPR) experiment that depends on three players' directional choices in the experiment. We define the players' moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.