Quantum and Classical Bayesian Agents

We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.