In a tennis tournament play 2017 players, each of them plays with the others 2016. A game can't be end at equality. If a player X beats the player Y in the direct game or beats a player Z who beats Y, this is happening for every Y, then X wins a trophy.
Show that there exists at least one player who wins a trophy.
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This is the king chicken theorem in another form. The existence of a "king chicken" (or a player that gets a trophy, in your terms) is Theorem 1 in the linked paper.
Assume for contradiction that there is no player X who wins a trophy.Then no matter what X we choose, there is a player Z who beats them.
Remove a random player X from consideration, leaving 2016 players.
Even with this reduced player size, there is still no player who wins a trophy, because if player Y won a trophy in this reduced case, he must also beat player X, as he beats a player Z who beats player X.Thus such a player Y would win a trophy in the full game, a contradiction.
Thus we have reduced the problem to one where there is 2016 players, and we can continue to do this down to the trivial case of 2 players, where there is clearly someone who wins a trophy, a contradiction.