競争 and 競技: competition and sporting events
Distinguish a competitive relationship from a defined event, and participation from winning.
Trying to get ahead
競争, read きょうそう, means competition. 二つの店が価格で競争しています。 says that two shops are competing on price.
競争が激しくなりました。 says that competition became fiercer. It does not report its end or identify a winner.
A sporting event
競技, read きょうぎ, refers to a sport, discipline, or event in which ability is tested under rules. この競技には十人が出場します。 says that ten people will compete in the event.
競技のルールを確認しました。 means checking the rules. Actually competing is a separate action.
Different scopes
競争 also appears outside sports, as in price competition between shops. For 競技, check whether the reference is to a discipline or organized competitive activity.
競技に出場しましたが、勝てませんでした。 means competing in the event but being unable to win. Participation does not become victory.
Is 二つの店が価格で競争しています necessarily a sporting event?
Show the answer and why
No. It describes price competition between two shops.