Quantum(-like) common knowledge: Binmore-Brandenburger operator approach

TL;DR

This paper extends the classical Binmore-Brandenburger approach to common knowledge into a quantum framework, using Hermitian operators to model agents' information and exploring the implications of noncommuting, incompatible representations.

Contribution

It introduces a quantum-like model of common knowledge based on Hermitian operators and extends the classical operator approach to the quantum domain.

Findings

Quantum analog of common knowledge features derived

Agents' information representations can be incompatible

Framework incorporates noncommuting operators

Abstract

We present the detailed account of the quantum(-like) viewpoint to common knowledge. The Binmore-Brandenburger operator approach to the notion of common knowledge is extended to the quantum case. We develop a special quantum(-like) model of common knowledge based on information representations of agents which can be operationally represented by Hermitian operators. For simplicity, we assume that each agent constructs her/his information representation by using just one operator. However, different agents use in general representations based on noncommuting operators, i.e., incompatible representations. The quantum analog of basic system of common knowledge features ${\cal K}1-{\cal K}5$ is derived.