In a tennis tournament, each competitor plays against every other competitor, and there are no draws. Call a group of four tennis players ``ordered'' if there is a clear winner and a clear loser (i.e., one person who beat the other three, and one person who lost to the other three.) Find the smallest integer $n$ for which any tennis tournament with $n$ people has a group of four tennis players that is ordered.

[i]Ray Li[/i]
1. **Show that 8 is sufficient:**
   - In a tournament of 8 people, each player plays against every other player. The total number of games played is given by the combination formula:
     \[
     \binom{8}{2} = \frac{8 \times 7}{2} = 28
     \]
   - Therefore, there are 28 wins and 28 losses in total.
   - By the pigeonhole principle, at least one player must have won at least 4 games. Let's call this player \(A\).

2. **Consider the group of 4 people that \(A\) has beaten:**
   - Let these 4 players be \(B, C, D,\) and \(E\). Within this group of 4 players, there are:
     \[
     \binom{4}{2} = \frac{4 \times 3}{2} = 6
     \]
     games played among them.
   - By the pigeonhole principle again, at least one of these players must have lost at least 2 games. Let's call this player \(B\).

3. **Verify the ordered group:**
   - Player \(B\) has lost to at least 2 players among \(C, D,\) and \(E\). Let's say \(B\) lost to \(C\) and \(D\).
   - Since \(A\) has beaten \(B, C, D,\) and \(E\), and \(B\) has lost to \(C\) and \(D\), we have an ordered group where:
     - \(A\) is the clear winner (beating \(B, C, D,\) and \(E\)).
     - \(B\) is the clear loser (losing to \(C\) and \(D\), and also to \(A\)).

4. **Show that 7 is not sufficient:**
   - Consider a tournament with 7 players. We need to construct a scenario where no group of 4 players is ordered.
   - One possible construction is:
     - Player 1 beats players 2, 3, and 4.
     - Player 2 beats players 3, 5, and 6.
     - Player 3 beats players 4, 5, and 7.
     - Player 4 beats players 2, 6, and 7.
     - Player 5 beats players 1, 4, and 6.
     - Player 6 beats players 1, 3, and 7.
     - Player 7 beats players 1, 2, and 5.
   - In this construction, no group of 4 players has a clear winner and a clear loser, demonstrating that 7 players are not sufficient.

Conclusion:
Since 7 players are not sufficient and 8 players are sufficient, the smallest integer \( n \) for which any tennis tournament with \( n \) people has a group of four tennis players that is ordered is \( \boxed{8} \).