Trying to understand how firms compete in the android store actually sounds like a great topic. Of course, we can only observe--at most--prices and sales per product, but it would be nice to think of how firms compete between each other and their reactions. My guess is that the biggest problem would be to find an identification strategy, like a change in the structure of the app store, so we can exogenize our regressors.
BTW, great job with AppNash, it looks very interesting!
If you want to talk more about the econometric approach, feel free to email me. Would love to chat more. If you discovered AppNash, then you can also figure out my email :). FWIW, your point about finding exogenous changes is right on (model = 2SLS), however getting the quantity sold data is not a simple procedure -- it's a matter of converting sales ranks to quantities. With out giving away all the secrets in public, here's a classic paper that guided some of my approach: http://www.business.illinois.edu/finance/papers/2003/chevali...
The original intent for my dissertation was the following: Chapter 1: Describe the theoretical framework of how to set up a system to automate the collection of data from an entire market (enabling the safe use of population estimators); Chapter 2: Apply that theory to analyze the app store data to test various firm- and product-level questions about the structure of strategies taken by firms (developers) in the app stores; Chapter 3: Another application of the theory using higher frequency data from the Internet (probably hotels, since hotels change their rates at the minutely/hourly level quite often, and regional hotel markets provide very well defined markets so new entry takes a while and is thus easy to account for).
BTW, great job with AppNash, it looks very interesting!