No. is the cardinality of set . If then this is not a finite 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?