Playing Games with Quantum Mechanics

TL;DR

This paper introduces a physical perspective on quantum games, emphasizing their playability and physical implementation, and distinguishes quantum from classical games by focusing on physical objects and actions involved.

Contribution

It proposes a framework for understanding quantum games through physical playability, offering a geometric approach to equilibrium and showing classical simulation of quantum games.

Findings

Quantum games can be viewed as families of playable versions.

Equilibrium conditions are derived for playable quantum games.

Quantum games can be simulated classically in terms of strategies and outcomes.

Abstract

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.