An introduction to multi-player, multi-choice quantum games

TL;DR

This paper provides a comprehensive, accessible introduction to quantum game protocols, covering two-player and multi-player scenarios, with focus on foundational concepts suitable for economists, game theorists, and physicists.

Contribution

It offers a self-contained overview of quantum game protocols and their general aspects, bridging quantum information theory and game theory for interdisciplinary audiences.

Findings

Introduces quantum versions of classic and multi-player games.

Explains formalism of quantum information theory relevant to games.

Highlights general features and potential applications of quantum games.

Abstract

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by a n-player generalization trough the quantum minority games, and finishing with a contribution towards a n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as an introduction suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.