What is a good marketing framework for an internet marketplace application

The concept you need to research and get your head around is called "the network effect." It means, as you have pointed out, that for the business to provide value for it's users, you need two groups using it in significant numbers.

Because you haven't provided any details, it is difficult to advise you what your options might be, but you can certainly look at other businesses that have faced this challenge and see what strategies they have used that have worked.

The 4P's will still apply to your marketing model but you have to address them within the context of the network effect.

Business Frameworks aren't some formula that you will feed in info about your product/service/business and get an answer. Essentially, a framework helps you structure your thought.

Now 4Ps is a very fundamental framework that helps you figure out and articulate 4 key things of your marketing mix. A good explanation is provided here http://www.netmba.com/marketing/mix/

Also since your web app would be something like a market maker - getting both sides of a transaction to meet, it would also do you well to look at Porter's 5 Forces framework (http://www.quickmba.com/strategy/porter.shtml). You could use it to analyse the business environment you are in and how you would like to use that environment to your advantage and what steps you would take to mitigate the risks inherent in that environment. A closely related framework would be the 5C's framework (http://www.netmba.com/marketing/situation/).

These would help you determine your business and marketing strategy.

And finally once you are done with all that, you can come to the mother of all strategy frameworks - the Hambrick's Diamond (http://www.provenmodels.com/598/strategy-diamond/donald-c.-hambrick--james-w.-fredrickson). It helps you in laying out the end to end strategy for your product (and not the whole business).

Hope this helps