I have a non-cooperative game involving a number of players. I computed the Nash equilibria which depend on a parameter $\alpha$. For $\alpha<\alpha_0$ there exist two Nash equilibria, e.g. $P$ and $Q$, for $\alpha=\alpha_0$ we have that $P\equiv Q$ while for $\alpha>\alpha_0$ we have only one of them, $P$.
Then, is $\alpha_0$ a bifurcation point? I'm asking because I know that the notion of bifurcation point is usually associated to ODE (or to a system of ODEs) that depends on a parameter, while in my case I don't have ODE (but players with utility functions).