compete against someone
to contend against someone; to play against someone in a game or contest. I don't see how I can compete against all of them. She refused to compete against her own brothers.
compete against something
to struggle against something; to seem to be in a contest with something. It was hard to be heard. I was competing against the noise of construction. Please stop talking. I do not wish to compete against the audience when I lecture.
compete for someone or something
to contend against or contest [someone] for someone or something; to struggle for someone or something [against a competitor]. They are competing for a lovely prize. Ed and Roger are competing for Alice's attention.
compete in something
to enter into a competition. I do not want to compete in that contest. Ann looked forward to competing in the race.
compete with someone or something
to contend against someone, something, or a group; to play in a competition against someone, something, or a group. I can't compete with all this noise. We always compete closely with our crosstown rivals, Adams High School.