Question: Represent the extensive form of the game:

Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively.

Then Player 1 chooses either Right or Left and does not observe nature's choice.

Finally, Player 2 chooses either G or H. Unlike Player 1, Player 2 observes the choice of Player 1 prior to making his choice. Player 2 also observes nature's choice if Player 1 has chosen Right but does not observe nature's choice if Player 1 has chosen Left.

My take: enter image description here

Is this correct? I am not really sure about the instructions in bold.

  • $\begingroup$ You pretty much disregarded the instructions in bold. What exactly is it that you are "not sure about" in that part? $\endgroup$ – Giskard Mar 2 '20 at 21:46
  • $\begingroup$ How to reflect that in the extensive form? $\endgroup$ – user508281 Mar 2 '20 at 22:31
  • $\begingroup$ With information sets where needed. $\endgroup$ – Giskard Mar 2 '20 at 22:50
  • $\begingroup$ Can you please be a bit more helpful? That is where I got stuck. $\endgroup$ – user508281 Mar 2 '20 at 23:03
  • $\begingroup$ Remember that nodes in the same information set of a player are nodes which the player cannot distinguish. Should there be any such nodes for Player 2 in your example? (i.e. are there any "situations" which Player 2 cannot tell apart?) $\endgroup$ – pegasus Mar 3 '20 at 2:04

Put player 2's decision nodes after a Left move by player 1 into an information set to concur with the description in bold. Here...

  • 1
    $\begingroup$ Downvote by me. I percieve these types of answers as giving the man a fish, rather than teaching them to fish (or do game theory). $\endgroup$ – Giskard Mar 3 '20 at 10:57
  • $\begingroup$ @Giskard, well, in some sense I understand the rule here to be: Give them fish, if they have shown at least a minimal amount of fishing effort. Might be a knife-edge case though... $\endgroup$ – VARulle Mar 3 '20 at 11:56
  • $\begingroup$ Knife-edge? What exactly is the effort made here? $\endgroup$ – Giskard Mar 3 '20 at 11:57
  • $\begingroup$ Also, ideally you never give the fish, I stick to teaching fishing when possible. $\endgroup$ – Giskard Mar 3 '20 at 11:58
  • $\begingroup$ @Giskard, the effort is in drawing a game tree that is almost correct, accompanied by text without typos and grammatical mistakes. That's considerably more than most of the pls-solve-my-homework questions here have to offer. As for fishing, well, there are different philosophies out there... $\endgroup$ – VARulle Mar 3 '20 at 13:51

Imagine you're Player 2. What different "scenarios" could you find yourself in?

  • If Player 1 chooses Right, then Player 2 could observe if Nature played Up or Down. So you have 2 information sets there.
  • If Player 1 chooses Left, then Player 2 couldn't differentiate between (Up, Left) and (Down, Left). How many information sets should there be here?

So in total, you should have how many information sets? You currently have 4. Which one should you "combine"?


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