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. (a) Draw a game tree for a game in which Hansel...

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.

(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?