Here is a problem in evolutionary game theory: (So the term I am using should be familiar for people in this field)
The game is called 'Clever Mutants' which is a symmetric two-player game:
For this game, I have managed to find three symmetric Nash Equilibria. They are $(a,a), (b,b)$ and $((1/4,3/4),(1/4,3/4))$, in which the first two are evolutionary stable (ES) and the last one is not.
Now, suppose that mutants have a 'secret handshake'. That is, suppose that mutants can recognize other mutants and play different pure strategies against normal and mutant opponents. For example, a mutant could play $b$ against another mutant but play $a$ against a non-mutant. Argue informally there can no longer be an $ESS$ (Evolutionary Stable Strategy) in which only $b$ is played.
I don't know how to argue for that statement, even informally. Can someone help me, please? Thanks so much.