If you compete with someone for something, you try to get it for yourself and stop the other person from getting it. You can also say that two people compete for something. 争夺
verb [vt. 及物动词]竞争,对抗;争夺;参加比赛
Hardware shops are competing fiercely for business. 各五金店正在为抢生意而激烈竞争。