3. [24 points] Benjamin Franklin once said, \"Laws too gentle are seldom obeyed; too severe, seldom executed.\" To ush out what he had in mind, the following game has three players: a lawmaker, a (typical) citizen, and a judge. The lawmaker chooses among a law with a gentle penalty, one with a moderate penalty, and a law with a severe penalty. In response to the law, the citizen decides whether or not to obey it. If she does not obey it, then the judge decides whether to convict and punish the citizen. Using Backward Induction, nd the values that the unspecied payoffs (those with letters a through I} can take to substantiate Franklin's claim by resulting in a lawmaker's choosing a law with a moderate penalty. HINT: The claim suggests that citizens do not obey gentle laws, and Judges do not convict if citizens do not obey severe laws. So, the objective is to nd values so that the equilibrium has the following properties: (1) when the law is gentle, the citizen disobeys the law even though he will be convicted; (2} when the law is moderate, the citizen obeys the law because he will be convicted; and (3} when the law is severe, the citizen disobeys the law because he will not be convicted. NOTE: Since payoffs are ordinal, you will only be able to state inequality relations between the uIISpecied payoffs and the numbered payoffs, or between the unspecied payoffs, on the game tree. Your answer should provide such relations only between the payoffs that are relevant considering the hint above. Punishments: Severe or Gentle? Do not Judge 8 Do not Do not Do not Convict Convict convict con vict con vicr