2010 IMO Shortlist 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)

$n \geq 4$ 玩家参加了网球锦标赛。任意两名选手只打一场比赛，并且没有平局。如果一个玩家被其他三名玩家击败，并且这三名玩家各自赢了一场比赛并输掉了另一场比赛，我们称四名球员为坏人。假设这次比赛没有坏公司。设$w_{i}$和$\ell_{i}$分别为第$i$个玩家的获胜次数和失败次数。证明 $$\sum_{i=1}^{n}\left(w_{i}-\ell_{i}\right)^{3} \geq 0$$ (韩国)