Indifference principle

Let ${\mathbf{p}}^{\ast }$ be a Nash Equilibrium and $i\in N$ be any player.

1. For every $s,t\in \text{spt}(p_i^{\ast })$ $U_i(s,{\mathbf{p}}_{-i}^{\ast })=U_i(t,{\mathbf{p}}_{-i}^{\ast })$
2. For every $s\in \text{spt}(p_i^{\ast })$ $U_i(s,{\mathbf{p}}_{-i}^{\ast })=U_i({\mathbf{p}}^{\ast })$