The reason they are ahead of their rivals is because THEY ARE BETTER
There isn't an anti-trust here, they aren't forcing you to buy a product, they aren't forcing you to use their search engine, and they aren't forcing you to do anything else with them. Everything they do is down to yoru choice.
Hey I know, while you're taking google to court for not pushing the products of their competitors, why don't you take apple stores to court for not selling the sony walkman or windows PCs.
Oh heres a good idea. Why not take Barack Obama to court for not following through with what the republicans promised.
Because doing either of those would make about as much sense.