I'm not so sure about this. When a market becomes consolidated ans stable enough, big players often decide to divide it and cooperate where possible, rather then compete fiercely. Look at the property, insurance and other stable markets.

What's the thinking behind such a strategy? Increasing the overall size of the market?

Well, you are sort of on the right track. If they interconnect the data even more, they'll make more money. Why is a merger that impossible in your books. It will be just business between two advertising companies.

Yes, but if they share their data with anyone else, it loses its value. That's why they go to such great lengths to collect all data on their own instead of working together.

Look at Google Analytics for the perfect example: Millions of websites help Google collect data, but they only ever get anonymized data in return. Google keep the valuable stuff to themselves.

Looks like this is already happening: https://news.ycombinator.com/item?id=12601471

It's a collaborated effort to develop an AI. Where did they announce that they'll share their user data?

So many clueless people are freaking out over this, completely ignoring the fact that sharing user data between companies like that would be highly illegal in many countries and get them fined to hell and back if they were seriously stupid enough to consider it, which they aren't.