What is $\times$ in the game theory notation (e.g. $\times_{j=1}^ns_j$)

Question

In game theory, I often see for a utility function $u_i$, $n$ players and some set of strategies $S$: $u_i:\times_{j=1}^ns_j \rightarrow \mathbb{R}$. What does $\times$ mean here? Is it literally multiplication, or something else?

Answer 1

$\times$ denotes the Cartesian product, i.e. $\times_{j=1}^ns_j$ is the set of all ordered $n$-tuples $(s_1,\ldots,s_n)$.