you're asking a loaded question.
the problem is laptop/hardware manufacturers RARELY produce what anyone in their right mind would consider a "gaming" laptop at that pricepoint. Oh sure there are laptops which can game fine in that price range, but the "gaming" laptops in that price range are almost universally junk.
This is the question i need to ask you, MUST you game in 1080p? Because if your answer is yes, i've got bad news. you're way under the budget you'll need to game in 1080p. If you don't mind gaming in 720p or 900p, then yes, there are laptops capable of gaming in those lowered resolutions in your price range.