compete for (someone or something)
To work or put forth effort against someone or something in an attempt to gain someone or something else. I refuse to compete for a guy's affections—if he likes someone more than me, then I need to move on. I'm feeling discouraged now that I know just how many people are competing for this job.
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.