I guess this depends on your view of the world. I would say that if you simply write a power function then that would indicate an arbitrary assumption to begin with, that has had to simplify a number of significant factors. Writing a power function might be simple, but I am not sure that it would be significant.

For example one view of the world would be at the surface layer, where you see the end result of a combination of small events. This is what I think you are doing with your power function, although I may be misunderstanding. Another view says that you will not worry about the surface layer, and will instead come up with a number of simple rules (some based on probabilities) for the various actions & interactions that can take place. The execution of the rules by the Agents over multiple turns gives the emergent behavior, or what I called the surface layer. If the surface layer emerges that you would expect (guns are better than knives in a war for example), then this indicates the model is hopefully not grossly off. So instead of getting one big function right, you instead have a number of small rules that determine actions and probable outcomes.

You could even play some games with determining probable power functions after running a number of these, by representing them as genetic strings and then doing standard genetic algorithms to see what gives the closest match over all the outcomes for the different scenarios/times. I think this is more powerful than starting with the power function because your assumptions are at a lower level that is easier to get right, not to mention simpler. This is also why I mentioned Epsteins book, its a great example of using simple rules to get emergent behavior.