ISL 2010 C5

$n \geq 4$ players participated in a tennis tournament. Any two players have played exactly one game, and there was no tie game. We call a company of four players bad if one player was defeated by the other three players, and each of these three players won a game and lost another game among themselves. Suppose that there is no bad company in this tournament. Let $w_{i}$ and $\ell_{i}$ be respectively the number of wins and losses of the $i$ th player. Prove that $$\sum_{i=1}^{n}\left(w_{i}-\ell_{i}\right)^{3} \geq 0$$ (South Korea)