At age two your child will show at lot of social development. But socially the child would wants to play alone. The child is more dependent on adult for guidance at this age. He or she will plays with dolls and start talking to them like you do with your child. The child will refers to self by name and will be socially very immature. He or she will learn the concept of others and will refer to them as people. The child may respond to only simple direction. So do not push your child to do more than his or her capacity.

I like this "plays with dolls and start talking to them like you do with your child" part. It is always enjoyable to watch a kid talking with her doll, giving advice, asking not to do this and that as if he/she is an adult. He/she seems like our copycat.

my baby girl is 2 years old and 4 months. she's very sociable and she does refer to herself by her first name. she likes her dolls and stuffed animals and treats them as like babies. this is fun for us both, and i really enjoy seeing her try to talk to her dolls/animals. this also enhances their imagination and communication skills too.