Markovian Agent Models: A Dynamic Population of Interdependent Markovian Agents

A Markovian Agent Model (MAM) is an agent-based spatio-temporal analytical formalism aimed to model a collection of interacting entities, called Markovian Agents (MA), guided by stochastic behaviours. An MA is characterized by a finite number of states over which a transition kernel is defined. Transitions can either be local, or induced by the state of other agents in the system. Agents operate in a space that can be either continuous, or composed by a discrete number of locations. MAs may belong to different classes and each class can be parametrized depending on the location in the geographical (or abstract) space. In this work, we provide a very general analytical formulation of an MAM that encompasses many forms of physical dependencies among objects and many ways in which the spatial density may change in time. We revisit recent literature to show how previous works can be cast in terms of this more general MAM formulation.