I think it is uncontroversial that, compared to standard economic theory, Agent-Based Models (ABMs) describe human behavior and market dynamics more realistically . This enhanced realism gives ABMs the potential to provide more accurate quantitative forecasts, once we figure out how to use them for prediction. However, if the goal of a model is more qualitative, for example to elucidate a theoretical mechanism, is realism useful?
Many economists would say that it is not, and too much realism may even be counterproductive. For example, to expose his Nobel-winning theory of asymmetric information (Market for Lemons), George Akerlof did not need boundedly rational agents and a detailed depiction of market exchanges. The standard setup, with rational utility-maximizing agents and market equilibrium, allowed a transparent exposition of the issue of asymmetric information. I think this is a fair point; however, which level of realism should be assumed in general qualitative models is mostly a matter of taste. If the modeler likes to highlight some economic force in a way that does not depend on people’s bounded rationality or on the nitty-gritty market details, then the assumptions of standard economic theory are okay. If the modeler wants instead to explain some phenomenon as the outcome of dynamically interacting boundedly-rational heterogenous agents, an ABM may be a more natural choice. In some situations, it may be the best choice.
Our paper “Residential income segregation: A behavioral model of the housing market”, with Jean-Pierre Nadal and Annick Vignes, just published in JEBO (Journal of Economic Behavior and Organization), is in my opinion a good example. In this paper, we study the relations between income inequality, segregation and house prices, and explore which policies best deal with these issues. Most urban economists address these problems using spatial equilibrium models. These models are solved by assuming that individuals in each income category experience the same utility all over the city; the resulting prices determine segregation. In our ABM, agents behave according to fast-and-frugal heuristics, and individual interactions dynamically determine prices and segregation patterns.
First of all, taking our approach provides simpler narratives. For instance, to explain why the rich live in the fanciest locations of a city, spatial equilibrium models need to assume that the rich care about city amenities more than the poor do. In our ABM, this is simply explained by rich buyers bidding up the prices until the poor cannot afford buying there.
Additionally, in our ABM it is straightforward to include as much heterogeneity as we need, as we do not have to solve for equilibrium. This is really useful, for example, to study the effect of income inequality on segregation. In accordance with empirical evidence, we find that stronger inequality increases segregation. However, it also decreases average prices over the city. Indeed, with stronger income inequality fewer buyers bid more, while most buyers bid less: the global effect is negative. Finally, we explore whether subsidies or taxes are better at mitigating income segregation. According to our ABM, subsidies are better, because they directly target the poor, increasing their purchasing power. Taxes instead hit the rich, but all benefits go to the middle class, with no effect on the poor. Modeling heterogeneity is key.
Finally, from a technical point of view, a standard critique from economists is that the reliance on numerical simulations in ABMs makes them less suited to clarify theoretical mechanisms. This is true to some extent. For example, the results in the paragraph above have been obtained by simulating the ABM . Nonetheless, we did solve parts of our ABM analytically, giving insights on the causal mechanisms within the model and on non-linearities. Maths and ABMs are not incompatible; the maths to solve ABMs is just a bit different from the one of optimization and fixed point analysis, more commonly used in economic theory.
In sum, I think that our paper is a good example of how even a qualitative ABM can be useful in economics, to provide more realistic narratives and to easily deal with heterogeneity. 
 Excluding some situations in which sophisticated agents interact strategically, such as Google auctions, where standard economic theory may be a more literal description of reality.
 To ensure full reproducibility of our results, we have put the code to generate all figures online on Zenodo, a Cern repository for open science. Sharing code is sn increasingly common practice in the ABM community, hopefully it will become the norm soon.
 For a version of this post with the figures from the paper, you can take a look at the Twitter thread starting from this link.