This thread reminds me of a conversation I had with a lady once on a training run. It seems we had different definitions of the word "competitive." She thought it meant going hard all the time and testing one's limits. I on the other hand, thought it meant you had a good chance to win or place high in a competition.
To answer the OP's question, I am not a competitive person unless I am in an actual competition. Now if someone such as the OP wants to make it a competition, then make it official and set the rules/parameters. I will still make it a friendly competition unless that person decides to run their mouth. At that point, I will do everything I can to destroy/humiliate them and make sure they never want to do it again.