Implement unique occurrence against each other
I think there are a few options for this, depending on the permanency of the effect:

Marker cards
Track the opposing cards that your card has faced on an object (e.g. Another card with the same title but instead of game text or an image it just has a list of the other cards and checkboxes, or just a section of each card that you mark).

Tracking sheet
If you use a separate object for tracking, like a score sheet or even just a piece of paper, it would be easy to track the cards you have played and the cards they have played against. 

There are still two major problems here: 


If the effect is permanent, you're eventually going to be unable to play a given card against any other card, placing a fixed lifespan on a copy of the game.
You're attempting to track a many-to-many relationship between cards, so depending on the size of your set this could be an extremely difficult task without some sort of spreadsheet or app or database to help.