Analysis of two-player quantum games in an EPR setting using geometric algebra

TL;DR

This paper explores two-player quantum games in an EPR setting using Clifford geometric algebra, analyzing classical and quantum strategies with specific examples like Prisoners' Dilemma and Stag Hunt.

Contribution

It introduces a geometric algebra framework to analyze quantum games in an EPR setting, highlighting the relationship between classical and quantum strategies.

Findings

Classical strategies are a subset of quantum strategies in this framework.

The analysis of Prisoners' Dilemma and Stag Hunt reveals quantum effects in strategic choices.

Abstract

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.