7. There are $n(n \geqslant 3)$ players participating in a table tennis tournament, where each pair of players competes in exactly one match with no ties. If player $A$'s defeated opponents are not all defeated by player $B$, then we say $A$ is not inferior to $B$. Determine all possible values of $n$ such that there exists a tournament outcome where every player is not inferior to any other player.
（Li Qiusheng, Contributed）
7. (1) When $n=3$, a tournament result can be constructed as shown in Figure 4, which clearly meets the requirements.
(2) When $n=4$, assume there exists a tournament result such that each player is not inferior to any other player. It is evident that no player can defeat all others (otherwise, the others cannot be not inferior to him), nor can any player lose to all others (otherwise, he cannot be not inferior to the others).

If each player defeats 1 or 2 others, suppose player $A$ defeats $B$ and $D$, and loses to $C$. Then, $B$ and $D$ must both defeat $C$ (otherwise, they cannot be not inferior to $A$). Thus, the loser between $B$ and $D$ (who only defeated $C$) cannot be not inferior to the winner (who defeated $C$ and the opponent).

Therefore, when $n=4$, there does not exist a tournament result that meets the requirements.
(3) When $n=6$, a tournament result can be constructed as shown in Figure 5.
(4) If there exists a tournament result for $n$ players where each player is not inferior to any other player, let the tournament result be represented by graph $G$. Then, add two players $M$ and $N$, and construct the tournament result as shown in Figure 6.
First, $M$ is not inferior to $N$, and $N$ is not inferior to $M$.
Second, for any player $P$ in $G$, since $P$'s defeated opponents include $M$ but not $N$, and $M$'s defeated opponents include $N$ but not $M$, $P$ is not inferior to $M$, and $M$ is not inferior to $P$; since $P$'s defeated opponents include $M$ but not $P$, and $N$'s defeated opponents include $P$ but not $M$, $P$ is not inferior to $N$, and $N$ is not inferior to $P$.
Therefore, this tournament result meets the requirements.
In summary, the set of $n$ that satisfies the problem's requirements is
$$
\{n \in \mathbf{N} \mid n \geqslant 3, n \neq 4\} .
$$