Difference between -i and j, when denoting other players (Game Theory)

Question

I do not understand the difference between -i and j in Game Theory. I have thus far been under the impression that they just represent two different styles of representing that the utilities, expected payoffs, strategies etc. belong to another player. But I have now encountered texts in which the authors switch between those styles (on the same page). For example (Tadelis, 2013, p.106) uses both. Which leads me to believe that the meaning is actually somewhat different. But how?

Answer 1

$-i$ is just a concise way of writing "all players other than $i$." This is very useful in games with many players, where it becomes quickly tedious to write up explicitly each player's index.

In games with two players, this notation is rarely used. In that case, typically one uses index $i$ to indicate player whose decisions are being analyzed, and index $j$ to refer to the other player.

If you type exactly the formula that confuses you, I can help you to decipher it.

Answer 2

$-i$ serves to denote all players except player $i$. It's something like saying all $j$ such that $i\neq j$.

If you just say $j$ you are referring to a particular player rather that to "all other players".