Yo Mama loses SOO many rap battles, the only thing that rhymes is her concession speech.
Two midgets fighting a battle with the most fearsome weapons they can lift; a brush and a fish-hook.
competition. Unlike the synonym 競争 （きょうそう）, 争う emphasizes a feeling of battle, a lack of rules, and only 争う can escalate to physical violence.
unless you're talking about a literal foot-race, 競争 does not mean a game. It refers to competing within a framework (usually business or academic). The best score on the test, the salesman who sold the most this month.
an argument or controversy