Constructing quantum games from symmetric non-factorizable joint probabilities

TL;DR

This paper introduces a framework for constructing quantum games using non-factorizable joint probabilities with symmetry constraints, enabling analysis of classical and quantum game outcomes without quantum formalism.

Contribution

It presents a novel method to formulate quantum games from joint probabilities, extending classical game theory to include quantum-like correlations.

Findings

New equilibrium solutions in quantum Prisoners' Dilemma, Stag Hunt, and Chicken games.

Demonstrates classical and quantum game outcomes within a unified probability-based framework.

Provides a general approach to analyze quantum games without quantum mechanics formalism.

Abstract

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.