Consider the prisoner's dilemma, in this game, you have a matrix,
$$A = \begin{bmatrix} (2,2) & (0,5) \\ (5,0) & (1,1) \end{bmatrix}$$
(or something like this)
But what is this object exactly?
Is $$A \in \mathbb{R}^{2^\mathbf{N} \times 2^\mathbb{N}}$$ I can't seem to know how to think about this object concretely.
I would say it’s a member of $(\Bbb R^2)^{2\times 2}$. If $A$ is some ring, $A^{2\times 2}$ is the set of two by two matrices with elements in $A$.