There is always a player such that every other player was either beaten by him or beaten by a player beaten by him

Every participant of a tournament plays with every other participant exactly once. No game is a draw. After the tournament, every player makes a list with the names of all the players, who either

(i) were beaten by him or (ii) were beaten by a player beaten by him.

Prove that there is a player whose list contains the names of all other players. (Hint: use the extremal principle )

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