A puzzle in game theory

Suppose that you do indeed have some contraband.  Deduce the correct response to this sign.

.Narcotics-checkpoint

Comments

I was going to post "It's a trap, the real check point is on the off-ramp." Then I read the article and felt less clever.

SPOILER:
Keep driving, it is a dummy sign designed to encourage smugglers to dump contraband.

Depends on how much drugs you have in your car...

Two of the indications that (as other commenters have pointed out) it is a fake sign is that

1) It is virtually impossible to have a drug checkpoint on a major highway without a traffic jam backing up at least half a mile

2) If there really were a drug checkpoint, there is no reason to put a sign warning drivers, especially if there is an exit. ("Be prepared to stop" is a flimsy excuse). I'm sure this is what Alex means by "a puzzle in game theory".

My response would be, "Glad I'm not one of those pot users who insists on taking the shit with them everywhere they go."

It's kind of a crafty way to get rid of drugs minus the expense of actual law enforcement efforts, the hassle of paperwork, etc.

This is a two-stage, two-player game with asymmetrical information. However, since neither player can observe the other's choice, it is played like a simultaneous game. You ask for game theory, so let's assume rationality.

Player A, "The Cops," is seeking to apprehend criminals with contraband. We assume their reward for doing so is compensation through fines levied (F) and public recognition (P). Each search of a vehicle costs salaried time or a police officer (T).

Player B, "The Driver," has the advantage of asymmetrical information. he either has drugs or he doesn't. Those with drugs do not want to be searched, due to loss of their drugs (D) and cash through fines (F). We will ignore the possibility of jail time, because it is likely a fringe scenario and complicates the calculation. If a player is stopped, regardless of drug possession, he also loses the search time (T). Note that we are assuming a standard value of time common between police and drivers.

The Cops have two choices: place the search on the main road (MAIN), or on the exit before the alleged search (EXIT). They must stop and search each vehicle that passes.

The Drivers WITH drugs have two choices: continue on the main road and hope the Cops are bluffing (MAIN), or pull off at the exit to ditch their drugs before returning to the road (EXIT).

Payoffs:

With Drugs:
[MAIN,MAIN] = (F+R-T,-F-D-T)
[MAIN,EXIT] = (-T,-D-T)
[EXIT,MAIN] = (0,0)
[EXIT,EXIT] = (F+R-T,-F-D-T)

We can already see that there is no Nash Equilibrium. The best strategic choice for the Drug Carrier is to use some sort of randomization strategy. The same applies to the Cops.

The next question is: what are the optimal randomization ratios according to the cost of time and value of fines, drugs and recognition? This analysis would have to take into account population percentage of drug carriers and population percentage of those 'innocent exiters,' since the Cops have to search everyone who passes by. If they choose [EXIT], they will have fewer cars to search, so could use a smaller force. Stopping every car on a main road would also impose a large social cost, but this would not be reflected in the Cops' individual decision process.

Also the value of the drug may impact the outcome. Could this be used to separate behavior of the high-stake drug carriers and low-stake? But that were the case we would likely have to reintroduce Jail penalties into the calculation.

Correction: since the value of T would be so high given the likely 99% proportion of innocents, overall the Nash EQ for cops almost definitely skews towards [EXIT]. I believe the optimal play is [EXIT,MAIN]. Or, as others pointed out, why would there even be a sign if there were actually a stop? It can be easily deduced that the cops are playing [EXIT].

The correct response is to pull over and scour the ground for free drugs.

At the end of the post, the original writer says "So, if you’re looking to take a trip anytime soon, take heed of the map below and, if you see one of these signs, don’t exit."

On the other hand, if you're clean, you owe it to all of us to exit and make the cops waste time searching you and your vehicle. Just think what a hoot it would be if an overwhelming number of clean citizens overloaded the checkpoint. And think how annoying it would be to the cops to see all those clean citizens drive across the road and right back onto the entrance ramp.

Enjoy your trip at home.

There is in fact a checkpoint on the highway leading out of the Rio Grande Valley in Texas going toward San Antonio that I have to go through all the time (which is what happens when you marry a Valley Girl), so I wouldn't have been so sure of its inauthenticity, knowing that there is such a checkpoint (where they also search for illegals).

Stop at the nearest donut store for bribes.

jonR, your comment is the best I've read. Thank you

Alger is right is you stop you will be canned

Interesting that so far nobody has mentioned the embarrassing misspelling. "Cheqeo" is incorrect.

I say "sadly" because it shouldn't be so easy for the police to violate our rights against unreasonable searches and seizures. There are plenty of legitimate reasons why someone would do a U-turn to get out of the line to avoid the fake, unlawful, unconstitutional drug search, so my point is that merely turning around shouldn't be probable cause. It's analogous to the police knocking at your door, without a warrant, and asking if they can search your home. If you say no, then do the police have probable cause? Of course not. And it would be sad if a court held otherwise.

Here in Houston, Texas, where I practice law, it's the death penalty capital of the world - about half the people on Texas' death row are from Harris County (Houston). And all the prosecutors are stereotypical jesus licking theocrats.

Finally, in a free and open society, there is no way to enforce a law that prohibits citizens from possessing certain leaves and powders while maintaining the original intent of the Bill of Rights. Study criminal law for any amount of time and you'll quickly realize that we have had a "drug exception" to the constitution ever since the "war on drugs" got started. The whole prohibition sceme is unconstitutional. It took a constitutional amendment to ban the sale and manufacture of alcohol (they never even tried to ban the mere possession of alcohol) yet to give the federal government the power to prevent me from simply possessing a marijuana leaf in my shirt pocket, it only takes a statute? The only way to explain that is that the constitution does not apply to drugs. And that's how we've been operating for 40+ years now.

"As Jesus said, it's more likely for a camel to pass through the eye of a needle than for a police officer to go to heaven."

I'm an atheist, and even I think this is a major-league dick comment.

There is in fact a checkpoint on the highway leading out of the Rio Grande Valley in Texas going toward San Antonio.As in all games of finite choices, there is always a Nash equilibrium in mixed strategies

I know the correct answer is supposed to be "take the exit." But I'm tempted to answer "recoil in fear at the ever-encroaching police state and the incremental disappearance of our liberties." At least one of those liberties is right to not be subject to an unreasonable search, and another important one is the ownership of your own goddamn bodies.

Not wanting to be searched is not probable cause for anything other than being a kick-ass American.

FYI: I live in New Mexico and there are so-called border checkpoints operated by the U.S. Border Patrol where they check for drugs (with dogs) and illegal aliens. The ones I routinely pass through are located: just north of Las Cruces, NM on I-25 with another further north at Truth-or-consequences; just west of Las Cruces on I-10; just west of Alamogordo, NM on U.S.highway 70 near the entrance of White Sands National Monument; east of El Paso, TX on I-10. Most days they will simply ask if all occupants of the vehicle are U.S. citizens and send you on your way and waiting times are short but sometimes the traffic back-ups can be horrendous. I have lived in this area 30 years and yes I had my vehicle searched once probably because I was young with long hair and a beard and therefore looked like a "hippie". (And no, they didn't find anything because there wasn't anything to find.)

"The correct response is to pull over and scour the ground for free drugs."

Indeed.

the topic is not about my position on the drug war, so therefore i'm not trying to convince anyone about the merits of my opinion on it. The topic is something totally different. As such, I feel free to speak the truth about the drug war rather than have to temper my comments to make them more palatable to the masses. Actually now that I re-read my comment, I didn't even say anything about my position on the drug war. I only commented on how I don't understand how someone can take an oath to uphold the constitution and then spend every waking moment of their job trying to minimize, marginalize, and utterly destroy the Bill of Rights (particularly the 4th Amendment). Regardless of whether I think drugs should be illegal or legally available by the pound at WalMart (the latter is my position, for what it's worth), the fact is there is no way to enforce laws against possession of ANYTHING consistent with the constitution. At least not aggressively, if someone commits a real crime and in the course of being arrested they are found to be in possession of contraband then in that scenario it would be constitutional to charge them with the possessory crime. But that's not how our government wants to fight the 'drug war' and it would mean anyone could get away with drug possession merely by not committing any other (real) crime. By "real crime" I mean an action like robbery, rape, murder, theft, assault, etc. There is no way the government can have probable cause to believe you have a banned leaf in your jacket pocket consistent with the Fourth and Fifth Amendments. So we've made exception after exception to those Amendments (particularly the Fourth, or "Swiss Cheese" Amendment) to allow for the prosecution of possessory drug offenses.

Every lawer responsible for those "exceptions" should be disbarred. Every politician responsible for those "exceptions" should be impeached. All lawyers and politicians took oaths to uphold, protect, and defend the Constitution. Making exceptions to the constitution is contrary to that oath. Merely arguing for an exception to the 4th Amendment should be automatic grounds for disbarrment.

Sadly? You think it is sad that the police would search someone who had clearly demonstrated probable cause of committing a crime? That is a very unique point of view.

I don't do drugs. I don't sell drugs. I don't associate with anyone who does.

I would probably take the exit, simply in order to avoid a possible traffic jam ahead... and according to you, that would be probable cause.

So, please tell me, why should someone who doesn't have anything to do with drugs, and acting 100% legally and rationally (i.e. avoiding a traffic jam), be searched? Why should I have to get the 3rd degree from the cops, why should my car get torn apart, when I have done nothing wrong?

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