...but competing with oneself is the essence of Budō.
Often heard question, after someone hears the other doing martial arts, is:
Do you compete?
Surely it is a valid question and easy one when martial arts are considered as a sport where competing is the essential part of the training routine.
The definition of a "martial art" is rather complex as it can also refer to the so called "fighting arts" or even to "fighting sport". Nevertheless, remember that the path is more than just training for competition.
A foreigner teaching karate in Japan has some nice insight on the subject.
Constant studying is what it is.