game theory, 70% game

[flopdanutz]

My game theory class for econ has 150 students.

last week the professor offered $10 to the winner of the following game.
Each student chooses 1 integer between 1 and 100 (1 being the minimum; 100 being the maximum). The professor calculated the winning number by taking the average of the numbers and multiplying that number by the ratio 7/10 (70% or 0.7). The student that gave the response closest to that number wins, in case of ties a student would be randomly chosen from the groups that tied.

What number would you choose and why? guess what number was the winning number? Do you think people think rationally?

I actually expect the results on this board will be drastically different from my econ class due to my perception that people here utilize game theory and strategic dominance more. The reuslts of the class outcome will be given later (after a few of you post)

[doormat]

This sounds like a great problem and I am sure someone will have a Bayesian Nash Equilibrium solution or a von Neumann epiphany or something that solves it. Since that is beyond my capabilities, I would approach it a different way. If you repeated this game over and over in a class of idiots, I would think the answer would get lower and lower. That is because if everyone was brain dead, the average guess would be around 50 and the winner would be 35. So the next time it is played, the idiots would guess 35 and the answer would be 70 percent of that, and so on. This would go on until everyone guessed 1 as the answer. So if everyone thought about it and credited everyone else with multi-level thinking, you might think everyone would guess 1. However, if everyone ties the winner is chosen at random, in which case you are no better off than when you started. Therefore I would guess 2 in hopes that all but a few give everyone else credit for carrying out the above thought process ad-infinitum.

doormat

[Copernicus]

Go back a week and you'll see a 50 post thread on the same thing.

[squiffy]

If people chose randomly, the average might be around 50 or 51. (This could be way off. Possibly 150 people selecting 150 random integers could give a very different average. I don't know how to do that math.)

But .70 (50) = 35. But if everyone can calculate this, then everyone will choose 35. If everyone chooses 35, then the average will be 35. Then .70 (35) = 24.

So thinking players would drive the average down to 1.

I think this is probably what ECON or MATH students might think.

But if you know that other people are all choosing 1, you can try to skew the statistics by choosing 100. So 149 people choose 1 and 1 person chooses 100 and the number is
still about 1.

But you don't know how many people will choose 100 or high numbers to skew the results.

So it goes in a big circle. And you cannot really guess what the number will be. Probably the numbers will end up being selected randomly. So I would just go with the original. Assume 150 random selections, take an average and .70 of that as your guess.

I guess the answer depends on how many levels of strategy you think people are likely to forsee and predict. And what percentage of the people will choose various strategies. I guess it is kind of a paper, scissors, stone problem with no right answer.

[squiffy]

Your optimal strategy would depend on how well you know your opponents and their level of math ability. If you were giving this to a bunch of homeless people or a class of kindergarteners, then you would assume random number choices. If you assume math whizes, it becomes much tougher.

[Nottom]

I don't know how to link to other threads but this same game was posted in the General Theory forum a couple weeks ago. Look for the threads "limitti's problem" and "an interesting problem", they generated a good amount of response.

[flopdanutz]

the winning number was 22
5 picked 1 (including myself)
5 picked a number greater than 70
5 people picked 22

I wish I had read the limitti thread before playing this game but i dont think i would have picked 22.

[MzLisa]

first, why do people have to be homeless or idiots, why cant u just pick a random number like he asked. To me its the same as guessing the number of jelly beans in a jar, and none of us take the time to really find out, we just pick a number.

Secondly, lets say that the first 100 students each picked a number 1-100, the first picked 1, second 2, the third person picks 3... 100th picked 100. now lets say that the remaining 50 started the count all over with 1. the 101 person would pick 1, the 102 person would, pick 2,....150th person would pick 50. I would calculated the results this way and come up with the average number.

[Copernicus]

[ QUOTE ]
why cant u just pick a random number like he asked.

[/ QUOTE ]

Like who asked? The professor asked for a number from 1-100, not a random one.

Why not pick a random one? Hmmm...because you want to win?

[doormat]

I wasn't using the term "idiot" disparagingly, Lisa. When I was brought up it was a scientifically accepted term for people with an IQ below 25, which seemed like a good arbitrary cutoff point for a group that might pick their number randomly, given the rules of the game. So let me rephrase it and use "logically challenged" instead.

doormat