I am reading a book about Game Theory and have just encountered the following definition of strictly dominated strategies:
Here is what I do not get:
- What does DS stand for?
- i denotes an arbitrary player (the amount of players goes from 1-n). Let's say that i represents player 1, how is this then valid to say:odd range? I mean, in the case that i denotes player 1, how can the range go from s1 to si(which in this case is 1)-1 when there is no player 0?
(DS) is a label for that inequality. Mathematical texts usually number equations to make it easier to refer back to them later on. If you look in the text, you'll find later something like: "In equation (DS)" or some other reference to the inequality, using that notation.
The notation that includes $i-1$ assumes you know that you can't plug in 1 for $i$ there; the point is to illustrate a property for one specific element of the tuple $s_i'$ and $s_i''$.