greeting other dogs/playing

Question
My 16/17 week old cairn terrier just went to the dog park for the first time today... I just wanted to ask some things about his behavior... Is it normal for him to be playing with another dog where they are both play biting and trying to bite each other's legs and stuff? They were also trying to dominate each other (I'm not sure if they were but from my observation they were). Is this normal?

Answer
YES that's perfectly normal behavior!  Dogs normally communicate clearly with one another regarding intention to play, although people often miss these (sometimes) subtle signals.  The real signal of a problem is when one dog suddenly misinterprets the play behavior of another and things start to get rough.  You would immediately perceive this as a problem, as your dog (especially a puppy of his age) would react with a pronounced fear response (a loud yelp and an attempt to get away.)  Try to closely observe any adult dog interacting with your puppy.  If you perceive the adult is getting too rough (the puppy yelps or shows fear), interfere CALMLY by stepping between the two and interacting with the ADULT (in order not to cause the puppy any more concern), then remove the puppy.  Most dogs "play fair" with one another, especially in dog exercise venues, but there are exceptions.  You might want to learn about dog body language so you can understand the communication being offered back and forth.