Brilliant game

In my Cognition and Culture class, we were asked to play this game.

Everyone was asked to write a number between 0 and 100 on a piece of paper. The winner will be the person whose number is closest to half of the average.
The above was told to everyone.

Brilliance:
Now, the question is which number to choose? If everyone chose randomly, the average (by law of large numbers) will be 50 and so its half would be 25. But everyone knows this fact. So everyone will choose 25. But if everyone chooses 25, then average is 25 and half of 25 is 12.5. So the person who guessed 12 would win it. But again if everyone choose 12, then half of average becomes 6. One can continue this series until one reaches 0.

But what number to choose?
Do you think your friends are smart(rational) enough to understand the above recurrence. Or are they simple morons (irrational) who would choose a random number between 0 and 100 without giving any thought to others.

Before reading the results, think of a number.

Results:
I chose 5 and i lost. The average was 20 and its half becomes 10. Winner was a person who chose 8.
The distribution was something like this. 2 people chose more than 50 (irrational), 2 chose 0 (the complete rational ones - Although it is still a question : Is it rational to assume that everyone around you is rational? I think no.)
Most people chose between 15 and 25 making the average 20.

I chose 5 with the assumption that there will be some morons but overall the class would be smart. I was wrong. There are more irrational people in class than i thought. Why some one would choose above 50 is beyond my knowledge.

Apparently, there has been a study by some researcher conducting the above in different groups to see if there exists any pattern. I am yet to find it.