Question 3: Playing an Honest Game
Two players, Ann and Bob, are about the play a board game. Ann gets to decide first if she wants to play
(P) or not (N). Only if Ann decides to play, then Bob gets to decide what game to play: Monopoly (M) or
Scrabble (S). Bob has two possible types. He is the 'honest' type with probability $p$ and he is the 'cheating'
type with probability $1 - p$.
If Ann decides not the play, then both players get a payoff of 0 (regardless of Bob's type). If they play
Monopoly, then both players get a payoff of 2 (regardless of Bob's type). If they play Scrabble, then the pay-
offs depend on Bob's type. Playing Scrabble with the honest Bob results in a payoff of 3 for Ann and 1 for
Bob. Playing Scrabble with the cheating Bob, on the other hand, results in a payoff of -2 for Ann and 4 for Bob.
Answer the following questions:
a) Draw a game tree to represent this game. Start with nature choosing the type for Bob, then proceed with
Ann's move, followed by Bob's move (if Ann chooses to play).
