my text defines player set as:
In N-player game $g$, each non-terminating node is partitioned into $N+1$ sets $g^0, ... g^N$. These are player sets.
However it makes no attempt to identify them on a figure.
For example, if we are given the following extensive form game
Each nonterminating node is partitioned into 2 sets, so N = 2 - 1 = 1. So our two player sets are $g^0, g^1$. Can someone please identify $g^0$ and $g^1$ on the game tree?
Thanks!
I think the idea is that a particular player set contains all the nodes in which a given player makes a decision. There are $N+1$ of them because there are $N$ players and then we consider nature as an additional random player. In your diagram, if we call Nature player zero, then $g^0$ would include just the initial node. $g^1$ would include both of P1's decision nodes. $g^2$ would include all four of the nodes at which P2 makes decisions.
The wording is a little off as it suggests that each node is partioned -- it would be a little more clear to say that each node belongs to a particular partition of the set of all nodes. The partition to which it belongs determines the player who acts at that node.
If you could also specify the text, I could perhaps confirm if my interpretation is correct.