To try and illustrate this in class I brought in 2 packs of cards. I actually ended up only using the cards as binary markers (whether or not they were facing 'UP' or 'DOWN'). I then proceeded to describe the following:
"If an UP card interacts with a DOWN card in any given round the DOWN card changes to UP on the next round. Otherwise everything else stays the same."
I used this game to illustrate how a strategy $\sigma$ can induce a population vector $\chi$ and I also touched upon what we would mean by $\sigma$ being stable.
We played the following games:
The left half the class was told to play UP and the other half to play DOWN. Thus our initial value of $\chi=(.5,.5)$. This was given by the fact that half the population was playing $\sigma=(1,0)$ and the other half playing $\sigma(0,1)$.