Sandeep and I are very close to finishing a first draft of our paper on torture. As I was working on it today, I came up with a simple three-paragraph summary of the model and some results. Here it is.
A number of strategic considerations play a central role in shaping the equilibrium. First, the rate at which the agent can be induced to reveal information is limited by the severity of the threat. If the principal demands too much information in a given period then the agent will prefer to resist and succumb to torture. Second, as soon as the victim reveals that he is informed by yielding to the principal’s demand, he will subsequently be forced to reveal the maximum given the amount of time remaining. This makes it costly for the victim to concede and makes the alternative of resisting torture more attractive. Thus, in order for the victim to be willing to concede the principal must also torture a resistant suspect, in particular an uninformed suspect, until the very end. Finally, in order to maintain principal’s incentive to continue torturing a resistant victim the informed victim must, with positive probability, wait any number of periods before making his first concession.
These features combine to give a sharp characterization of the value of torture and the way in which it unfolds. Because concessions are gradual and torture cannot stop once it begins, the principal waits until very close to the terminal date before even beginning to torture. Starting much earlier would require torturing an uninformed victim for many periods in return for only a small increase in the amount of information extracted from the informed. In fact we show that the principal starts to torture only after the game has reached the ticking time-bomb phase: the point in time after which the deadline becomes a binding constraint on the amount of information the victim can be induced to reveal. This limit on the duration of torture also limits the value of torture for the principal.
Because the principal must be willing to torture in every period, the informed victim concession probability in any given period is bounded, and this also bounds the principal’s payoff. In fact we obtain a strict upper bound on the principal’s equilibrium payoff by considering an alternative problem in which the victim’s concession probability is maximal subject to this incentive constraint. This bound turns out to be useful for a number of results. For example the bound enables us to derive an upper bound on the number of periods of torture that is independent of the total amount of information available. We use this result to show that the value of torture shrinks to zero when the period length, i.e. the time interval between torture decisions, shortens. In addition it implies that laws preventing indefinite detention of terrorist suspects entail no compromise in terms of the value of information that could be extracted in the intervening time.
Cheap Talk 
9 comments
Comments feed for this article
May 19, 2010 at 3:04 pm
michael webster
How will your model account for the fact that some people after being tortured simply give up any information, whether real or false, to stop the pain?
May 19, 2010 at 9:19 pm
jeff
that’s another difficulty with torture, but one that seems straightforward enough that a model isn’t needed to examine that particular problem. our goal is to shed light on the less obvious difficulties.
in terms of the model, we assume that the torturer is only interested in information that he can use. any other information, in particular unverifiable cheap-talk, is treated by the torturer as no information at all and does not stop the torture.
May 21, 2010 at 11:42 pm
Ryan
haha… cleverly put response.
May 19, 2010 at 11:40 pm
John
This is ridiculous. Don’t take your predetermined conclusions, make assumptions to make sure you get to your preferred conclusion, write a paper about it and pretend that you are an academic.
For shame. This is a travesty. I thought economists were better than this.
May 20, 2010 at 9:10 am
jeff
Thank you for your input John.
To clarify, everything in the first paragraph is a conclusion, not an assumption. Those “strategic considerations” are intermediate results that are used to build intuition so that the main results are easy to understand and interpret.
In case you are interested, the key assumption is that the principal will not torture a victim he knows to be uninformed. Here is the paragraph that describes the model.
We study a dynamic model of torture where a suspect/agent faces a
torturer/principal. In the model there is a “ticking time-bomb:” the principal
wants to extract as much information as possible prior to a fixed terminal date.
Each period, the principal decides whether to demand
some information from the agent and threaten torture.
The suspect either reveals information or
suffers torture. This continues until either all of the information is
extracted or time runs out. We characterize the unique equilibrium of this game.
May 20, 2010 at 9:41 am
michael webster
“The key assumption is that the principal will not torture a victim he knows to be uniformed.”
Hmm, that is interesting. So does the victim know this also? Or can he try to fake being uniformed?
May 20, 2010 at 11:25 am
jeff
Indeed he will try to fake being uninformed. And that is the whole point of torturing him. Because if he really is informed he will want to give up information to avoid being tortured.
May 20, 2010 at 11:28 am
Does Economic Theory Assume Its Conclusions « Cheap Talk
[…] on A Summary of the Torture …jeff on A Summary of the Torture …John on A Summary of the Torture …Ryan on Should You Hit “Reply Al…jeff on A Summary of the […]
May 25, 2010 at 9:27 am
michael webster
Jeff;
Take a look at one of the last scene’s in the Godfather, where Michael Corelone is trying to get his brother-in-law to confess as to his role in killing Michael’s brother earlier in the movie.
He threatens violence, but he get his confession with minimal effort. How does your model deal with this example?