*Hades sleeping with a rubber ducky*
Even thought rats may live in cages they also need time out of their cages to play and bond with their human. I take my boys out at least 30 minutes 3 times a day. Sometimes more especially when others are taking them out to play. Ken loves to take them out and when my daughter comes over she'll sometimes take them out and let them run around too. They love coming out to play. You can tell they want to because they'll be running back and forth or hopping on the bars at the front of the cage and will crawl right onto your hands when you open the cage.
Sometimes when they get older they'll still want to come out but instead of running around playing, they just want to be held and cuddled. I had a few rats that would fall asleep on my shoulder, my lap or even in my shirt.
That was Romi and she slept like that on me all the time. A few of the others liked that place to sleep as well and I never minded.
I always tell people who are adopting rats for the first time that if you don't have the time they need for play time you should really think about getting an animal that doesn't require your time, like a gold fish.