Feedback and chaos make this a far harder problem than you let on.

As a chaotic system develops over time, tiny initial differences are amplified, making it increasingly intractable to predict behavior even with complete knowledge of causality. (Weather has elements of chaotic behavior.)

A system with feedback (and agents) alters its behavior in the future based on the current behavior of agents. These systems can be arbitrarily complex and even simple scenarios can require agents to take strategies that are not strictly individually rational in order to obtain a good outcome ("superrationality").

Simply having a tough time ruling out causal factors in a complex system is a heck of a lot easier than these.