Rosen's condition ([J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33(3):520–534, 1965][1]) for uniqueness of the Nash Equilibrium in n players game states that the equlibrium will be unique when:

1. payoff function $\pi(\textbf{s})$ of every player is concave in own strategy
2. There exists vector $\textbf{z}$ ($(\forall i \in N)(z_i \geq 0)\ \wedge (\exists i \in N) (z_i >0)$ such that function $\sum_{i=1}^{n}z_i\pi_i({\textbf{s}})$ is diagonally strictly concave

$N$ denotes the set of players. What is the intuition behind diagonal strict concavity condition? [1]: http://www-inst.eecs.berkeley.edu/~ee228a/fa03/228A03/papers/rosen.pdf