Game Theory in Categorical Quantum Mechanics

TL;DR

This paper explores how categorical quantum mechanics provides a high-level, topological framework for understanding quantum information processes and extends this perspective to quantum game theory and Bayesian games with quantum correlations.

Contribution

It introduces a novel approach to express quantum game theory procedures using categorical quantum mechanics and investigates the connection between Bayesian games and Bell non-locality.

Findings

Quantum game procedures are represented using topological semantics.

The connection between Bayesian games and Bell non-locality is analyzed.

Categorical quantum mechanics offers a unifying high-level perspective.

Abstract

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\cite{AC}, \cite{Co}, \cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \cite{BL}.