On the equivalence between non-factorizable mixed-strategy classical games and quantum games

TL;DR

This paper investigates the conditions under which classical game-theoretic models can be transformed into quantum games, focusing on non-factorizable probabilities and their implications for strategic interactions.

Contribution

It introduces two approaches for creating non-factorizable games and analyzes their equivalence to standard quantum games, highlighting limitations and mathematical conditions.

Findings

Non-factorizable probabilities characterize quantum games.

Standard quantum games can be analyzed as non-factorizable games.

Limitations of the non-factorizable approach are identified.

Abstract

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question, is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analyzed as a non-factorizable game and determine the limitations of our approach.