What are the problems Microsoft having buying Activision and Blizzard, if Activision and Blizzard want to sell themselves, How would anyone be able to cancel the deal, just like what Sony is doing?

The issue is monopolies. If a company becomes too large or absorbs too many ‘rivals’ in a certain space the deal can be blocked because it would create a monopoly. A monopoly is bad because it gives the company that holds it too much power to charge what they like, be uncompetitive in quality, and quickly overwhelm or buyout any new rivals that appear.

In this case I believe the issue is that Microsoft would become too dominant in the game publishing space. Obviously Sony have a vested interest in keeping that from happening but they can’t just block it on the grounds of “I don’t like it”, they need a valid case which is what’s now being investigated.