There is no problem with installing games on an ssd providing your ssd has sufficient capacity.
Typically users will install Microsoft Windows 7, software applications, utilities, and favorite games on an ssd. Additional games, data files, videos, images, music, documents, and backups are stored on a hard disk drive if the ssd does not have sufficient capacity. Games can be swapped between the ssd and the hard drive.
How large an ssd were you planning to get?