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 enter image description here

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?



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.

| cite | improve this answer | |
  • 1
    $\begingroup$ Ah much clearer. It is a course text...and in the figure drawn there were no distinguishable nodes (dots or otherwise) just lines...and the payoffs are at the place where the player 2 nodes should be. $\endgroup$ – Bajie Aug 27 '15 at 23:37
  • $\begingroup$ I can see why it confused you -- I had to think about it for a moment also as I'm not in the habit of defining player sets, though it's a natural enough thing to want to define. $\endgroup$ – Shane Aug 28 '15 at 1:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.