My son and his wife have a dog. They do not carry the dog (about 80 lbs) to his bed every night, but they do tuck him in, cover him up. When he has stayed with us, I have been known to be sure he was covered on his blanket, on his designated end of the couch (he’s not allowed on furniture at their house, and only the one spot in ours).
Our cat will hang out with me while I get ready for bed each night, and then go downstairs as soon as I get in bed. So every night, I go downstairs and retrieve him from whatever spot he has selected, and bring him back up to the bed, where he usually stays for most of the night. It is kind of “our game”, and he seems to totally expect and anticipate that I will come looking for him each night.
I never thought about that, but you are right about it being a game. They like the personal attention so they go off and lay down far away, knowing you will get them.