Are all kids competitive by nature, or is it a learned behavior?

A few weeks ago, my daughter (who is 2) was showing off her "special blanket" to her cousins, who are 4 and 7. The four year old replied with "I have more blankets than you do." Followed by the 7 year old who said "I have more blankets than both of you." I was pleased that my daughter responded with an enthusiastic "Yeah!", instead of getting in on the competition. Fast forward to the next weekend when we were going shopping, and I asked my daughter what she wanted to look for and she said "A new blanket". I didn't think much of it until we were in the car, and she said "Gracie [her slightly younger cousin, who is also 2] only has one blanket."

So, my sweet little daughter was trying to one-up her little cousin! My question is: is this something normal that kids do - compete with each other to always try to have the most or be the best? Or were my nieces just being bratty, and my daughter picked up on their behavior? Just curious as to what your experiences have been, and what I have to look forward to as my daughter gets older!