There could be some kind of point system in the tournaments.

Double elimination is almost always a better idea than single elimination in tournaments. If not double elimination, then I think each match should be played "best out of 3".

Anyhow, the point system could work the following way:

You get a set amount of points each time you win and lose a smaller amount of points each time you lose.

Let's say: Win = 2 points, Lose = -1 and Draw = 0.

Then, an additional number to your points is added equal to the highest level card you play with. So playing with a level 10 card = 10 additional points from the start.

The winner of the tournament get a card with a level equal to his/her total amount of points divided by 2. In this case, winning 5 matches and losing 0 and playing with a level 10 card would earn you 20 points, which would be the minimum requirement for getting another level 10 card.

...well, something like that. Just off the top of my head.