1. Suppose two players, First and Second, take part in a sequential-move game. First moves first, Second moves second, and each player moves only once.
(a) Draw a game tree for a game in which First has two possible actions (Up or Down) at each node and Second 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 First and Second 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 First has four possible actions (North, South, East, or West) at each node and Second has two possible actions (Stay or Go) at each node. How many of the two node types are there?