7. There are 10 chess players participating in a round-robin tournament (i.e., each pair of players competes in one match). The rules state that a win earns 2 points, a draw earns 1 point for each player, and a loss earns 0 points. After the tournament, it is found that each player's score is unique, and the second-place player's score is $\frac{4}{5}$ of the sum of the scores of the last five players. What is the score of the second-place player? $\qquad$
7. 16 .

The last five contestants have to play 10 matches, so the total score of the last five contestants is greater than or equal to $2 \times 10=20$.
Thus, the score of the second-place contestant is greater than or equal to
$$
\frac{4}{5} \times 20=16 \text {. }
$$

The score of the first-place contestant is less than or equal to $2 \times 9=18$.
If the second-place contestant scores 17 points (i.e., 8 wins and 1 draw), then the match between the first and second-place contestants must be a draw. This way, both the first and second-place contestants would score 17 points, which contradicts the rule that each contestant has a unique score.
Therefore, the second-place contestant scores 16 points.