Not to the extent that humans can. My chinchillas are fascinating little rodents. If I give one a treat, s/he will immediately accept it and run off to eat it in private. Sharing never crosses that little rodent mind. On the other hand, I often wonder if there isn't some semblance of politeness in running off, so as not to brag they have something another doesn't. One day, the male had to go to the vet. It wasn't a pleasant experienced, and when I brought him home, he huddled in a corner of the cage. The female went over to sniff him, then ran off to the other side of the cage. She dragged one of the hay feedbags over to him.
Anyway, I am in no way downplaying animals or the animal kingdom, but humans clearly have something in addition to what other animals have.