Consider the extensive form game depicted in figure 13.5.
(a) Would it make any difference to the analysis of this game if we removed the information set of player 2 that links the topmost and bottommost pieces of the tree? If so, what difference? If not, are there information sets of player 1 that are similar candidates for removal?
(b) Analyze the prior distribution over the four possible initial nodes. Suppose we say that player 1 is "rational" if one of the top two of these initial nodes prevails, and player 2 is "rational" if one of the middle two initial nodes prevails. Is there correlation in the rationality of the two players? Is the correlation positive or negative?
(c) Analyze this game. Assuming this model describes a particular situation, do you think you can clearly predict what will happen?
