Sunday, August 23, 2009


Finding an Actual Use for My Game Theory Training

Although my dissertation was in capital and interest theory, my "field exam" at NYU was in "theory," which basically meant micro/game theory. This was definitely an example of studying something for its sheer elegance, because I think whenever game theorists pontificate on the actual real world, they usually give horrible advice. (E.g., "Yes, sir, it would be a good idea to build hundreds of nuclear warheads for the U.S. government, but only if we deploy them according to this formula.")

But yesterday I actually benefited from my years of training. On the radio there was some goofy commercial with kids on a road trip. The kids are bored and the brother says, "Let's play 20 Questions" and the sister immediately agrees and throws out the first question. So there was no way the brother could have had time to think of his pick, before hearing the question about it.

So that got me to thinking: Would there be an advantage to either player, doing it this way? In other words, if someone says, "Let's play 20 Questions!" should you immediately blurt out a question, before the person can think up his pick? Or does it give an advantage to the other player, because then he can choose the thing based on your question (and then answer appropriately of course)?

At first, I thought there was no way to really answer this definitively. But then I realized that actually, the answer is straightforward, and all you have to do is make a very weak assumption that wouldn't even upset Murray Rothbard on a good day.

I leave it to the reader as an exercise.

Is the solution to your puzzle bigger than a breadbox?
Here's a big hint: The weak assumption that I'm hoping wouldn't even upset Rothbard, is that the person who has to first think of the thingie, has the ability to ignore the question he hears and pick something as if he hadn't heard the question.
How could he ignore the question? Why would anyone ask a question and not demand an answer?

I think what Bob means is that the person thinking of the thing can ignore the question - if he so desires - when he makes his pick.

Which actually makes the answer somewhat obvious, as I think about it... though I'm not sure that we're still in "Game Theory world"...
Yeah, but how could he ignore the question without lying? If you lie then you would be found out in the end when you gave your answer. So I'm still stumped on how this would benefit you. I always thought the point of your questions is to divide the world, and I don't see how, if you ask the right kind of questions, it would benefit anyone in this scenario.
OK for anyone who is still checking this, this is what I had in mind:

Let's say Billy says, "Let's play 20 Questions!" and his sister Sarah says, "OK, is it a person?"

So the question is, does Sarah's blurting out the first question give her, or Billy, an advantage?

My answer is that if it has any effect at all, it is to help Billy, so long as we assume that he can pick his thingie without being influenced by Sarah's question. (Now that assumption might be false; maybe by saying "person" she makes him more likely to pick a non-person, and Sarah is awful at guessing people so her ploy works.)

But anyway, let's assume that Billy can use whatever process he normally would have, to generate his first pick, without being influenced by Sarah's question. In that case, Sarah's blurting out can't possibly help her, because Billy can guarantee himself the same expected outcome as if she hadn't blurted out the question. I.e. he can generate his first pick the normal way, and then honestly answer Sarah's question as if he's hearing it for the first time.

So, the only reason Billy would allow himself to be guided by Sally's question, would be if he thought it would give him an advantage to do so. And since this is a zero-sum game (i.e. Billy's advantage is the same as Sarah's disadvantage) then Sarah's blurting out of the question can at best do nothing, and at worst hurt her.

Last point, I should add that in my ten-second musing in the car, I didn't realize that really I must have been talking about the expected advantage or disadvantage. As I typed out the above, I realized that I initially had assumed (without realizing it) that Billy understood Sarah's abilities, and so he would be able to tell if considering her question (when making his pick) would help him or her. But if Billy doesn't know Sarah's strengths and weaknesses in 20 Questions, then he might not be sure.
Two more clarifications:

1) There aren't 3 siblings in the above; I typed "Sally" once instead of "Sarah."

2) Really what I'm doing with the above is not a full-blown analysis, I'm just using a shortcut to box the answer in. What I'm saying is, so long as we assume Billy has the ability to generate his first pick while ignoring Sarah's question, then we know her move can't help her, at least in the sense that doubling down on a 16 while the dealer shows an Ace is not going to help you. (I.e. you might end up winning 2x as much money, but with the information you have at the time of your decision, it's a stupid move.) So I'm not going through the hard work of spelling out exactly how it hurts her; I just know that it must, because Billy has the ability to neutralize her move if he decides that's his best response.
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