How can I detect if my function is receiving an instance of it as a parameter? (Javascript, details down below)

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Javascript

HTML

game

BACKGROUND
So this is a game with my friends I am playing. You create a function in the form of f(them), where them is the opponent function. What the game does is pit both functions against each other in a game of prisoners' dilemma, but with access to the other's function. However, as you can see above, the function is "wrapped" by another function, so ToString() and name do not work. You cannot alter the stack either.

QUESTION
How can I detect when my bot is playing against myself? (I need that info because the bots also play against themselves, and for extra points in this game, I want it to cooperate with itself for extra points.)

Source code:
https://pastebin.com/8Dx2hppZ
Edit fiddle - JSFiddle[^]

What I have tried:

I have tried invoke counters, and creating tester functions that don't return 'C' or 'D'. They have not worked.