Analyzing three-player quantum games in an EPR type setup

TL;DR

This paper employs Clifford Geometric Algebra to analyze three-player quantum games in an EPR setup, exploring how different entangled states influence game outcomes and strategies.

Contribution

It introduces a GA-based framework for analyzing multi-player quantum games in an EPR setting, including various entangled states and classical-quantum strategy comparisons.

Findings

GA provides a clear analysis of quantum game outcomes

Different entangled states affect players' strategies and payoffs

Classical strategies are embedded within the quantum framework

Abstract

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.