Taxonomies in the area of Multi-Agent Systems (MAS) classify problems according to the underlying principles and assumptions of the agents’ abilities, rationality and interactions. A MAS typically consists of many autonomous agents that act in highly complex, open and uncertain domains. A taxonomy can be used to make an informed choice of an efficient algorithmic solution to a class of decision making problems, but due to the complexity of the agents’ reasoning and modelling abilities, building such a taxonomy is difficult. This paper addresses this complexity by placing model representation, acquisition, use and refinement at the centre of our classification. We classify problems according to four agent modelling dimensions: model of self vs. model of others, learning vs. non-learning, individual vs. group input, and competition vs. collaboration. The main contributions are extensions of existing MAS taxonomies, a description of key principles and assumptions of agent modelling, and a framework that enables a choice for an adequate approach to a given MAS decision making problem.