We distinguish between two main types of model: predictive and explanatory. It is argued (in the absence of models that predict on unseen data) that in order for a model to increase our understanding of the target system the model must credibly represent the structure of that system, including the relevant aspects of agent cognition. Merely “plugging in”an existing algorithm for the agent cognition will not help in such understanding. In order to demonstrate that the cognitive model matters, we compare two multi-agent stock market models that differ only in the type of algorithm used by the agents to learn. We also present a positive example where a neural net is used to model