There are a number of players you'll find in the game who have a competitive streak.. Most of them have a higher aggression rating, low composure etc, and often pick yellow cards, senseless ones.. and also at times pick up the red jeopardizing the team's chances..
even if the instructions are for them to stand off, not to jump into tackles etc, I have seen a few players picking up a yellow per game, or something close to that.
I am asking what do folks do with such players, irrespective of their talent.. do you prefer to sell them?
I for one sell them sooner than later, and prefer having a team with more composed players..
Competitive streak has nothing to do with the visible attribute, but with the Dirtiness hidden attribute. Higher his dirtiness, the more 'competitive' he's willing to be, i.e. dives, trying to use his hands, etc. It can be good depending on how you play. Yes, ideally no one should cheat but it will happen from time to time. The more prominent dirty players will be aggressive, but it's more a correlation than causation. Dirtiness in tandem with Sportsmanship and Temperament is what generally governs the yellows/red from diving, violent tackles, etc than Aggression and Composure.
Comes down to how you play, if you want to really emulate Simeone or Mourinho's Inter, then you may want those competitive players.The more abrasive you want to play, Dirtiness acts as a positive modifier at the risk of cards.A dirty, unsporting player is good in an abrasive system.
However, if you don't want to be abrasive and want your best players always available you'd want to avoid Dirty/'Competitive'/Unsporting players. Either way, you want them to have high Temperament.
You can "fine" them when they receive red cards, it should reduce their "Aggression" attribute
Fining a player affects their Temperament stat and not their Aggression stat. You can be aggressive and not lose your cool, however Aggression does increase the risk of cards indirectly as more aggressive players will be more willing to get into tackles. More tackles means a greater likelihood of getting a card, but Aggression by itself doesn't directly cause increased cards. If you have an aggressive player who has good Tackling, Anticipation, Concentration, and Decisions they'll get less cards than an equally aggressive player with lower stats in the other attributes. However, fines are generally only effective when they are justified and the player is professional enough.