06.08b Putting a Murdered Corpse in a Rental Storage Unit-- Game Theory. . I think I might have heard about this crime story from the WSJ's Best of the Web.

"It Takes One to Know One"

The body of a woman missing since 1990 was found stuffed inside a container at a rental storage unit, and authorities charged her then-boyfriend with murder," the Associated Press reports from Syracuse, N.Y.:

George W. Geddes Jr. was ordered held without bail Monday in the death of Margaret Reome, 31. . . .

Last summer, local authorities learned that Geddes was renting the 5-foot-by-5-foot storage unit. But it wasn't until last month that they realized he had not reported it to federal officials as required by the terms of his probation, Sheriff Kevin Walsh said.

The FBI obtained a search warrant.

"I don't think there's anybody in law enforcement who would think a defendant would be that stupid to keep a dead body in a storage shed rented under his own name," District Attorney William Fitzpatrick said. "Luckily, people like this keep us in business."

OK, Geddes was pretty stupid--but how smart are the law-enforcement guys who took 14 years to figure this out?

This could be used for a game theory problem for the fourth edition of my book. Here is an outline.

1. Why can't it be equilibrium rational behavior for either criminals to always keep bodies in sheds rented under their own names or police to always search sheds rented by criminals?

Answer: If criminals always put bodies in sheds they rent, the police will always catch them, so the criminals would deviate. If police always search the sheds, the criminals will never put bodies in them, so the police would deviate and safe their efforts by not searching.

2. Why can it be equilibrium rational behavior for criminals sometimes to keep bodies in sheds rented under their own names and police sometimes search sheds rented by criminals?

Answer: A mixed strategy equilibrium.

3. Suppose some police and criminals are stupid, choosing actions that do not maximize their expected payoffs. Does there still exist a mixed strategy equilibrium?

Answer: Maybe--it all depends on magnitudes. If the number of stupid people is low enough, the mixed strategy equilibrium still exists. If it is high enough, it does not---if, for example, 99% of police never search even if all criminals hide bodies, then the 1% probability of getting caught may not be enough to outweigh the cost of finding a more obscure hiding place.

4. Would the police like to commit to always searching sheds?

Answer. Maybe. This would deter use of the sheds, raising the cost of crime. But it would mean fewer criminals caught by searching sheds, paradoxically enough. Figuring out the answer would take more analysis than I want to do right now.

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