You can buy a new laptop for $400, but it will only have integrated graphics which can be good enough for some games, but may not be good enough for the games you want to play.
At $400 you are basically looking at an older used laptop with dedicated graphics. I recommend you consider the following Dell Latitude 3540 "Business Laptop" with a 4th generation dual core i5-4210u and Radeon HD 8850m GPU (competes directly with the GTX 660m) for $335. The least expensive laptop on ebay with the GTX 660m is $500 but it did have a 3rd generation quad core i7 CPU.
Are you okay with going used? New "gaming" laptops don't really exist around 400 dollars, hard to find anything new with a halfway decent or any dedicated GPU in that price range.
You can buy a new laptop for $400, but it will only have integrated graphics which can be good enough for some games, but may not be good enough for the games you want to play.
At $400 you are basically looking at an older used laptop with dedicated graphics. I recommend you consider the following Dell Latitude 3540 "Business Laptop" with a 4th generation dual core i5-4210u and Radeon HD 8850m GPU (competes directly with the GTX 660m) for $335. The least expensive laptop on ebay with the GTX 660m is $500 but it did have a 3rd generation quad core i7 CPU.
I actually have this laptop. I bought refurbished back in early 2014 somewhere between $475 and $500. It is pretty decent. The Radeon HD 8850m is ranked a little better than the more modern nVidia 940mx at Notebookcheck.net. Click link below to see game benchmarks. The most demanding game I played with that laptop is Fallout 4, but only at 1600x900 resolution using medium graphic settings to get something like 40 FPS to 45 FPS most of the time, if I remember correctly.