Abstractions in Causal Models and Game Structures

We investigate abstractions in causal and strategic models of multi-agent systems, exploiting the relationship between these models. The paper contains two main results. The first one demonstrates that abstraction in causal models is a faithful correspondent of abstraction in strategic models, i.e., for a given causal model, if we generate a corresponding strategic model and abstract this model, we will obtain the same model as when we abstract the causal model first and then generate its corresponding strategic model. The second result is that a causal dependency in an abstract (high-level) model entails a causal dependency in the original (low-level) model. This allows us to reason about causes in a simpler abstract model and derive conclusions about causality in the much larger low-level model. These results set the stage for studying and using abstractions of causal models in multi-agent settings.