Definition of finite strategic game

Hello, I'm just trying to make it clear that what a finite strategic game is.

The definition of it in my book has this form:

Let G be a strategic game. We say that G is a finite game if, for each player i, |A_{i}|<**∞**, where A_{i} is the strategy set of player i.

If I let A_{i} be a subset of R^{n}, does |A_{i}| mean the measure of A_{i} in R^{n}?

For instance, if A_{i}=[0,1], an interval of R for all i, then is G a finite game?

Re: Definition of finite strategic game

No. $\displaystyle |A_ix|$ is the cardinality of set $\displaystyle A_i$. If $\displaystyle A_i= [0, 1]$ then this is not a finite game.

Re: Definition of finite strategic game

A finite strategic game is a static model that describes interactive situations among several players.