© 2015 Wiley Periodicals, Inc.Computer models can help humans gain insight into the functioning of complex systems. Used for training, they can also help gain insight into the cognitive processes humans use to understand these systems. By influencing humans understanding (and consequent actions) computer models can thus generate an impact on both these actors and the very systems they are designed to simulate. When these systems also include humans, a number of self-referential relations thus emerge which can lead to very complex dynamics. This is particularly true when we explicitly acknowledge and model the existence of multiple conflicting representations of reality among different individuals. Given the increasing availability of computational devices, the use of computer models to support individual and shared decision making could potentially have implications far wider than the ones often discussed within the Information and Communication Technologies community in terms of computational power and network communication. We discuss some theoretical implications and describe some initial numerical simulations. © 2015 Wiley Periodicals, Inc. Complexity 21: 202–213, 2016.