Equal but different

Discrete Mathematics Level 5

In a round robin tournament with \(N \) teams, every 2 teams play in a head-to-head match. Points are awarded as follows: 3 points for a win, 1 points for a tie and 0 points for a loss.

What is the smallest value of \(N\), such that it is possible for all the teams to have the same number of points, but for (at least) two teams to win a different number of matches?