### I Suck With Websites

So I wrote this little two page note on a game theory paper called the traveler's paradox, but I don't know how to post it on here. I slipped it under the door of the one game theorist who teaches at BSU, but he hasn't gotten back to me, so I thought maybe somebody who has taken game theory could help me out. First, however, does anybody have suggestions on how to post it?

Also, a great post on torture over at marginal revolution: http://www.typepad.com/t/trackback/2388722. My question is how do the torturers behave?

Without knowing how much information the prisoner has, how far do you go? It seems to be an optimal stopping problem: you choose the amount of information you want before hand and keep going until you get that info. Notice here that the prisoner could be lying, but you stop once you hear the required words. If this is how a prisoner thinks the captors behave, I would go with MR's first option as being the prisoner's optimum (since this prisoner is a willing confessor).

The above seems like a poor solution, since the captors do not differentiate between good and bad information. Now what if you wish to maximize the ratio of "good" information to "bad" information. Furthermore, suppose that you expect that the probabilities of getting "good" and "bad" information as a function of time are both increasing, but what can you say about their ratio? It seems that here you would get torture even if the captive told the truth right away.

It seems that to discuss the captor behavior one needs to differentiate between different types of prisoners: Cooperative and Uncooperative. Then differentiate between types of information: True or False. Then the problem is to determine probabilities of getting C-Prisoners and U-Prisoners. Then we might assume that P(TrueC-Prisoner)>P(TrueU-Prisoner) and think from there about the above ratio problem... I have all summer to mess around with these things, though, so I'm going to go to bed now.

Also, a great post on torture over at marginal revolution: http://www.typepad.com/t/trackback/2388722. My question is how do the torturers behave?

Without knowing how much information the prisoner has, how far do you go? It seems to be an optimal stopping problem: you choose the amount of information you want before hand and keep going until you get that info. Notice here that the prisoner could be lying, but you stop once you hear the required words. If this is how a prisoner thinks the captors behave, I would go with MR's first option as being the prisoner's optimum (since this prisoner is a willing confessor).

The above seems like a poor solution, since the captors do not differentiate between good and bad information. Now what if you wish to maximize the ratio of "good" information to "bad" information. Furthermore, suppose that you expect that the probabilities of getting "good" and "bad" information as a function of time are both increasing, but what can you say about their ratio? It seems that here you would get torture even if the captive told the truth right away.

It seems that to discuss the captor behavior one needs to differentiate between different types of prisoners: Cooperative and Uncooperative. Then differentiate between types of information: True or False. Then the problem is to determine probabilities of getting C-Prisoners and U-Prisoners. Then we might assume that P(TrueC-Prisoner)>P(TrueU-Prisoner) and think from there about the above ratio problem... I have all summer to mess around with these things, though, so I'm going to go to bed now.

## 1 Comments:

Andy -- if you've not yet gotten feedback, and still want to post the paper, let me know. I can post it as a file on the website I post to (Truckandbarter.com) and can provide you with the direct link for the file (so people can link to the file from your site) and a quick post on the site. I'm always eager to read game theoretic stuff, so I figure it's a good way to spread the joy.

If you feel like it, let me know at ian@thesitementionedabove.com.

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