CMO 1987 Problem 3

Some players participate in a competition. Suppose that each player plays one game against every other player and there is no draw game in the competition. Player $A$ is regarded as an excellent player if the following condition is satisfied: for any other player $B$ , either $A$ beats $B$ or there exists another player $C$ such that $C$ beats $B$ and $A$ beats $C$ . It is known that there is only one excellent player in the end, prove that this player beats all other players.