Rafael Robb: What is the probability that as the "defendant" you are totally screwed?

Guy murders his wife over the Christmas break. She was going to divorce him and collect a lot of alimony. This happens in tony King of Prussia, Pennsylvania. He tries to stage the scene to look like a break-in and robbery. It takes the police under two weeks to figure out the scheme: He's got a weak alibi, there's broken glass improbably breaking over the body (after the crime), and the wife's body looks like her head's been torn off by a shotgun (it's not, it's just his rage).



Now get this. The guy's an economics professor at U Penn. He teaches a course in Game Theory and his final take home exam is still available online. Take a look at the exam and ask yourself, for a guy so smart, did he ever consider the odds?

Economics 682
Game Theory
Final Take home Exam
Rafael Robb

5. Consider the following signaling game. There are two players, a plaintiff and a defendant. The plaintiff knows ahead of time whether he will win the case if it goes to trial, but the defendant does not. Instead the defendant considers the probability of the plaintiff winning to be 1/3. (Formally, nature chooses whether
the plaintiff wins or losses, and reveals this information to the plaintiffs only. The probability that nature chooses "win" is 1/3 and the defendant knows it is 1/3). All this is common knowledge. If the plaintiff wins his payoff is 3 and the defendant payoff is -4. If the plaintiff losses his payoff is -1 and the defendant's payoff is 0. These payoffs are also common knowledge.

The plaintiff has two possible actions: demand a low settlement amount, m=1, or a high settlement amount m=2. If the defendant accepts a settlement demand of m, the plaintiff's payoff is m and the defendant's payoff is m. If the defendant rejects theplaintiffs demand, the case goes to court.