8. Consider the following game in extensive form. B 2 Н. 1,1,1 1,1,1 J K 9.1.1 LM 1,9,3 2,1,8 NO 4,2,1 1,3,4 5,2,1 4,3,2

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8. Consider the following game in extensive form. B 2 Н. 1,1,1 1,1,1 J K 9.1.1 LM 1,9,3 2,1,8 NO 4,2,1 1,3,4 5,2,1 4,3,2 (a) (5 points) There is something wrong with this game tree. (It is not a proper game tree for some reason.) Can you say what is wrong with this tree? Why? Find a way to make the tree a proper extensive form game tree. Explain. Hint 1: Suppose there is nothing wrong with the nodes, the payoffs, the branches, and the information partition of the tree.) (Hint 2: There could be more than one way, but you just need to find a way.) Answer the following questions after making the tree a proper extensive form game tree. (b) (5 points) How many subgames are there? (c) (10 points) Draw the normal form representation of the extensive form game. (d) (10 points) Find all of the pure strategy subgame perfect Nash equilibria of this game.