com·pete 
(kəm-pēt)
(kəm-pēt)intr.v. com·pet·ed, com·pet·ing, com·petes
To strive against another or others to attain a goal, such as an advantage or victory. See Synonyms at rival.
[Late Latin competere, to strive together, from Latin, to coincide, be suitable : com-, com- + petere, to seek; see pet- in the Appendix of Indo-European roots.]