Nash Equilibrium contd.

Let xi equal S for player i and x-i equal S for all other players

IFF player i ∈ {1, … n} chooses strategy xi then payout function = fi(x) ;

it follows that x* ∈ S will produce a Nash Equilibrium such that

∀i, xi ∈ Si : fi(xi*, x-i*) ≥ fi(xi*, x-i*)