Case Studies for a Markov Chain Approach to Analyze Agent-based Models

Abstract. Agent-based models have become a widely used tool in social sciences, health care management and other disciplines to describe complex systems from a bottom-up perspective. Some reasons for that are the easy understanding of agent-based models, the high flexibility and the possibility to describe heterogeneous structures. Nevertheless problems occur when it comes to analyzing agent-based models. This paper shows how to describe agent-based models in a macroscopic way as Markov chains, using the random map representation. The focus is on the implementation of this method for chosen examples of a Random Walk and Opinion Dynamic Models. It is also shown how to use Markov chain tools to analyze these models. Our case studies imply that this method can be a powerful tool when it comes to analyzing agent-based models although some further research in practice is still necessary.