Nash equilibrium

In a game with $n$ players where player $i$ has choice of strategies in $S_i$. The state $(s^{\ast}_1, s^{\ast}_2, \ldots, s^{\ast}_n) \in S_1 \times S_2 \times \ldots \times S_n$ is in Nash equilibrium if for all $i$ we have

$$s^{\ast}_i = \mbox{arg}\max_{s_i \in S_i} U_i(s_1^{\ast}, \ldots, s_{i-1}^{\ast}, s_i, s_{i+1}^{\ast}, \ldots, s_n^{\ast}).$$

Where $U_i$ is the utility function for player $i$.