Is Share for Share an effective way to increase activity on a page?

I am at 37k fans right now and this is a strategy I have never used. Mainly because you have to find a page with similar amount of likes and most pages below 30k it's not effective at all anyways.

My theory is the people who actually see your posts is people with lower friend count where their news feed isn't all cluttered with things other than pages. Or people who constantly like your content. So my theory is when you share for share those people who luckily see your content your giving them another competitor to compete with. So those valuable fans you have your possibly giving them away to another page in exchange getting some also but most likely just hurting you in the end.

Anybody a big fan of this strategy? I understand it could increase my amount of likes but at this point I want activity>likes... Thanks =)

Its not Like that and yes s4s does increase you fan activity as well as likes it is useful and if someone likes your post and you share some one else's post on your page doesn't mean he is always going to like your competitor page and its upto the users to decide if you keep thinking like this then i don't think you can ever grow your page in terms of likes as well as activity

okay, here's the deal,
Do not Share the " page link " it's better to share a picture from that page, and ask him to share a picture from yours,
that would give better result to ( Talking about + some more extra fans )
if you want you can make on page " seo " i will post something about that in new thread, stay updated