The primary changes in common knowledge that occur as a player asks another player for a card are that everyone knows the asking player does not have that card at that point and that one of the two other players is confirmed to have it once it has been asked for: if it is still possible that the asked player does not have it, only the third player can still have it: The other two do not have it and one of the three of them must have it. In addition to this, the player reveals he or she has at least one of the other three cards out of the category the asked card was from. If the asking player does not have the physical card from that category, this means he has ensured one of his blanks is of that category.
If the same player asks for different cards from the same category later, the possible cards the blank could be will become more limited and if three different cards from the category are asked for by the player, the blank must be the fourth card from the category. If the card owned by the asking player is not the physical one, one of his opponents (the one not owning the actual physical one) will not yet be sure which card the asking player owns while his opponents are, unless the physical card has already changed hands once in the game. In that case, he knows the asking player does not own the physical one, and therefore is sure which card the asking player has as well.
The situation becomes even more complex once the limited amount of blanks each player owns and the randomly distributed physical cards need to be taken into account. A full simulation going over possible game sequences and capable of using multiple strategies would be required to fully analyse the knowledge changes and test strategies.