🚀 go-pugleaf

In preparing a book, I ran into the following problem: How should I
typeset "Player A"?  Should it be Player A or should it be Player $A$?

My inclination is not to add the dollar signs for the following reasons:

a. The A is not a mathematical entity. It is a name for the player, like
   Player Abraham. Alternatively, it is an enumeration part, like
   Player 1, Player 2, etc.

b. Graphically, I find it unpleasent to have a somewhat slanted $A$ together
   with the unslanted Player.

My co-author prefers $A$, claiming that it better stressed this way.

I looked at several books on the subject and they all use a slanted A,
or italic A. However, Player 1 was always printed with no slant, or italics.


My questions are: Is there a correct way to typeset Player A?
                  If not, what do you prefer personally, and why?

Thanks in advance for every answer and advise you may care to give,

Michael