Although the y50 is a VERY good choice for a gaming laptop, 300~400$ more isn't exactly "a little bit more"...
In any case, if you're strictly allowed not to go higher than 700$, I'd go for Proofy's suggested Acer. It's true that both that and the ASUS sport an 840M, which is a fine entry-point for laptop gaming (mind you, a 740M would be more than OK too), but that ULV CPU will probably bog the performance down on a 1080p resolution IMO. Best if you go with the other one, which sports a maximum res of 1366x768.
1080p on a 15" laptop looks very nice for games, but desktop usage can be tiring for the eyes, as objects become rather small...I can vouch for that, having just lately bought an HP Envy on sale sporting an i5-4200M and a GTX 740M. The 1080p desktop kinda takes its toll on my eyesight...
If you can afford to stretch for a medium price increase (about 150$) and want the 1080p with better chances of running at decent framerates, this is also a very viable choice
http://www.newegg.com/Product/Product.aspx?Item=N82E16834152570.
If you can afford the huge price increase (as I've already said, about 300~400$), Thetechmech's adviced y50 will be one of the best choices, although if you can stretch that high with budget, your best bet would be customizable laptops, like
iBuyPower's.