(Game Theory) Suppose Andy and Brian are playing a guessing game.

\fSuppose Andy and Brian are playing a guessing game. There are two slips of paper; one is black and the other is white. Each player has one of the slips pinned to his back. So, two possibilities: (1) Andy gets the black slip while Brian gets the white slip (2) Andy gets the white slip while Brian gets the black slip. Assume that nature chooses each of these two possibilities with probability 1/2. Neither player sees the paper on his own back, but assume that the players are arranged so that Andy can see the slip on Brian's back, but Brian doesn't not see Andy's slip. So, Andy learns which of the two possibilities nature has chosen but Brian does not. After nature's decision and Andy has seen the slip on Brian's back, the players interact as follows. First, Andy chooses between Y and N. If he selects Y, then the game ends; in this case Andy gets a payoff of 10 if nature has chosen (1) and -10 if nature has chosen (2), and Brian gets a payoff 0 regardless of what nature has chosen. If Andy chooses N, then it becomes Brian's turn to move by choosing between Y and N, ending the game. If Brian chooses Y and nature has chosen (2), then Andy obtains 0 and Brian obtains 10. If Brian chooses Y and nature has chosen (1), then Andy obtains 0 and Brian obtains -10. If Brian chooses N, then both players obtain 0 regardless of what nature has chosen. (a) Describe this game in extensive form. (Remember that the tree has to describe all the information including probabilities and any information set.)