International Law

Applause Auction

Image by MarkWallace via Flickr

Interesting little puzzle, as reported by Niranjan Rajadhyaksha at Livemint.

"Avinash Kamalakar Dixit likes to play a game or two--even as he teaches game theory to his students at Princeton University.

There is an old Princeton tradition that Dixit uses to bring to life what can sometimes be an esoteric and math-heavy subject.

Students at that university thank a teacher with a polite and brief round of applause when he finishes a course with them.

From that comes the "applause auction", which is now part of the folklore of economics. Dixit pays anything between $20 and $50 to the student who claps last.

So there is an incentive to keep the applause going. Most students drop out of the game after 15-20 minutes, says Dixit.

The record is four and a half hours. Often, there is more than one student in the running for the prize, sometimes as many as five or six. These students learn to compete and collaborate among themselves, and how people and organizations do so is the central quest of game theory.

But, Dixit's contribution to game theory--the science of strategy--goes far beyond this strikingly original way of teaching it."

Interesting game. Why does anyone drop out by themselves? The clear strategy is for the class to collude together - clap for 5 minutes and then have everyone stop. If anyone continues to clap, they cannot do better for themselves, but they can make everyone worse off.

What if the rules only allow one winner? Perhaps the winner is picked at random from those who stopped clapping at the same time? Well, the collusion strategy is still the best expected strategy - but now, there is an incentive for someone to try to steal the pot by only pretending to be part of the collusion.

In either case, however, I suspect that the success of the collusion strategy depends upon how badly any individual would feel being ostracized by the group for defecting from the collusion strategy.

My sense is that defection would not be in general more prevalent in the second game. If the group has seen the value of the collusion strategy, and realize that they can all get an equal chance at the prize and leave early, this team coordination might be enough to defeat the defection intention.

Be a good experiment to run.

Full post as published by Misleading Advertising Law on October 17, 2008 (boomark / email).