Suppose two players, Hansel and Gretel, take part in a sequential-move game. Hansel moves first,…

Suppose two players, Hansel and Gretel, take part in a
sequential-move game. Hansel moves first, Gretel moves second, and each player
moves only once.

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(a) Draw a game tree for a game in which Hansel has two
possible actions (Up or Down) at each node and Gretel has three possible
actions (Top, Middle, or Bottom) at each node. How many of each node
type—decision and terminal—are there?

(b) Draw a game tree for a game in which Hansel and
Gretel each have three possible actions (Sit, Stand, or Jump) at each node. How
many of the two node types are there?

(c) Draw a game tree for a game in which Hansel has four
possible actions (North, South, East, or West) at each node and Gretel has two
possible actions (Stay or Go) at each node. How many of the two node types are
there?

 

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