Classical vs Quantum Games: Continuous-time Evolutionary Strategy Dynamics

TL;DR

This paper compares classical and quantum evolutionary game dynamics, introducing a new quantum formalism and demonstrating potential advantages of quantum strategies over classical ones in game scenarios.

Contribution

It unifies evolutionary game theory with quantum strategies and presents a novel quantum evolutionary dynamics formalism.

Findings

Quantum strategies can outperform classical strategies in certain game settings.

The paper establishes a formal connection between classical and quantum evolutionary dynamics.

An example shows quantum strategies yield higher rewards against classical strategies.

Abstract

This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We then introduce a new formalism of quantum evolutionary dynamics, and give an example where an evolving quantum strategy gives reward if played against its classical counterpart.