I am reading the book Game Theory: A Multileveled Approach Second Edition by Hans Peters. It appears to be the most recent copy. I've search here and on Google for a list of known errors in the book, but couldn't find any.

In section Sequential Battle of the Sexes there is a decision tree in figure 1.1. The tree looks like this:

recreation of figure 1.1 from Game Theory by Hans Peters

Setup (paraphrased from the book) The Story here is similar to the original Battle of the Sexes only this time we assume that man chooses first and the woman can observe the choice of the man.

I am new to game theory. I'm trying to make sure I understand this and I'm not missing something. Should the rightmost decision tree of player 2 be F(B) not F(F) (I hope I worded that right)? I started to think that maybe I didn't understand the difference between the two scenarios (the woman knows what the man chooses vs. she doesn't know). Thanks for any help.


You are correct. It should be $F$ and $B$ on the right side subgame just as it is on the left. It looks like it's just a typo in the book that both are labeled $F$.

In terms of understanding it, keep in mind that a strategy for P2 defines what she would choose at each of her information sets. Here, she has two information sets, so her strategy set is $S_2 = \{FF,FB,BF,BB\}$, where, by convention, the first letter denotes the action she will choose if P1 chooses $F$ and the second letter denotes what she will choose contingent on P1 playing $B$.


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