The Odds Of Getting Caught

There's a problem that goes by a number of different names, depending on where it's found: Prisoner's Dilemma, the Tragedy of the Commoms, the Fishery Problem, etc. The problem occurs whenever a number of different people share something that can be used up, but none of them own it or control it. As an example, the blue crabs of the Chesapeake Bay were once plentiful. Since no one owned them, anyone could catch and sell them, and everyone did. Now there aren't enough blue crabs left to provide watermen with a living. Pollution also played a role, but the biggest problem was overfishing. Since no one owned the crabs, no one had any incentive to limit their catch to sustainable levels. Only the states of Virgina and Maryland had the power to limit catches, and they were under constant pressure from the watermen to keep the catch limits higher than sustainable levels.

The problem occurs whenever it is to everyone's advantage to protect a resource by not abusing it, but it is to each individuals advantage to cheat. In the case of blue crabs, it is to the watermens' advantage if they all cooperate to protect the blue crab, but it is to each individual's advantage if they cheat and catch as many crabs as possible while everyone else follows the rules. The result is that everyone cheats, and everyone is harmed.

Something similar happens in strip clubs. A strip club owns something valuable; a license to operate as a strip club. The club gets to keep the license as long as it's employees don't break any laws. The violations most likely to cause a license to be revoked are liquor laws and prostitution laws. And the people who might violate the prostitution laws are the strippers. Unlike Chesapeake watermen, club managers can enforce cooperation by firing cheaters. But enforcement is never completely effective; a minority of strippers continue to sell sex.

For a prostitute, working in a strip club has advantages. She doesn't have to worry about the sort of violence that only occurs when there are no witnesses. She doesn't have to advertise; the club does the advertising for her. The risk of arrest is reduced; if a customer has bought a few dances, the odds of him being an on-duty policeman are much lower. And while she's waiting for someone to buy her sexual services, she can make money from dances.

For a girl who don't want to admit that she's a prostitute, being a stripper provides her with an odd sort of alibi; she's not really a prostitute, she's just a stripper who does extras. If a guy buys a dance, she upsells him to the VIP room. If he's in the VIP room, she upsells him to sex. Or she uses sex as an inducement to upsell him to the VIP room. Or better yet, he begs her to let the him pay for sex. She's just doing it because the customers pressure her into it.

So for some strippers, the advantages of cheating outweigh the advantages of cooperation. A single violation doesn't increase the club's risk of losing its license very much. Their only concern is the risk of getting caught by a manager. They're pretty certain that they're not going to get caught, and they probably wouldn't if they only did it once.

Let's say a stripper/prostitute provides sexual services during one out of every twenty encounters with a paying customer, or 5% of the time. She's directly observed in the VIP room by a manager four times out of one hundred encounters, or 4% of the time. She has a 4% chance of getting caught each time she has sex with a customer, which is the same as saying that she has a 96% chance of not getting caught. Using a binomial distribution, the odds of getting caught rise to 19% if she has sex five times over 100 encounters, and to 56% if she has sex twenty times over 400 encounters. In other words, the more times she has sex with a customers, the more likely she is to get caught, which seems pretty obvious. But each individual time she has sex with a customer, the odds of getting caught are only 4%. So each time a customer offers $100 for sex, she's weighing that $100 against a 4% chance of getting caught, which is the same thing as a 96% chance of not getting caught. $100 and a 96% probability of not getting caught sounds like pretty good odds. If she's someone who lives moment to moment, or if she's under pressure to earn a lot of money quickly, she may not make the conceptual leap from a one time safe bet to an aggregate risk that rises as the number of violations increases.

Assuming that it takes a while for managers to catch and fire the strippers who sell sex (the cheaters), I'm curious about what effect they have on the strippers who don't sell sex (the cooperators). My guess is that while the cheaters attract customers the cooperators would rather not deal with, they also help the cooperators earn more money. If a customer comes into a club with the expectation of buying sex, he may know that some of the strippers are prostitutes, but he doesn't know which ones. To get a stripper to talk to him, he has to pay for her time. So he ends up spending money on a few cooperators before he finds a cheater (prostitute). Once he figures out who the cheaters are, he no longer has to spend money on cooperators, but the turnover in strip clubs tends to be high, so he still has to spend money on new strippers before he figures out who the cooperators and cheaters are. And many customers never seem to learn; they keep trying to buy sex from strippers who have repeatedly refused them in the past.

The thing I don't understand is why someone would go to a strip club hoping to hire a prostitute. Hiring an escort seems like a lot less work. Some people will tell you that the combination of alcohol and naked girls is enough to explain anything, but some other possible explanations are:

• It's a two step process: they go to the strip club for the strippers, but once they're there, they get aroused and start wanting a prostitute.
• They're using the strip club as a way of fooling themselves into believing that they're not really trying to buy prostitutes.
• What they really want is an old fashioned brothel, where men could get entertainment, alcohol, conversation, and prostitutes all at the same place. In the US, brothels are illegal but strip clubs come close, offering strippers instead of prostitutes, so they go to strip clubs and act as though they were in a brothel.
• They just can't learn.