I've been trying to find all the Nash equilibria for a 2-player game with 2 actions either, where the payoffs were dependent of variables. I'm finished, except for one special case (I had to divide by something and pretend it's not zero). Now I want to consider that case.
If I do, I get a game where the outcomes for both players and both strategies is just 0.
Does that mean that there infinitely many Nash equilibria? So if I called my strategies $p^\ast = (p,1-p)$ and $q^\ast = (q,1-q)$, will there be a Nash equilibrium for all $(p,q) \in [0,1]^2$? Wouldn't that also mean that all pure strategies would be pure Nash equilibria?
Thanks in advance for the answer.