Nash Equilibrium and $20

Searching the New York Times I found the following article that is intriguing. It is a professor that auctions a $20 bill (similar to what Joe Baker demonstrates in his economics class).

There are eight students that participate in the silent bid. The students all engage in “co-opetition” both competing and cooperating. The options before them would be to bid together or against each other. If they bid together they all come out winners. If they bid against each other, only one would win the money (and the amount pocketed depends on the bid). I find it interesting that instead of creating a large Nash Equilibrium matrix with eight people making separate decisions, they decided to bid the same price. The only exception was Ashley who chose to bid on her own. In essence, there became two parties, the seven with the same price and Ashley.

I like this article and example because it shows the various choices before people and how they react to situations.


Jayden said...

Great article, Colin. The reader comments on the article are good, too. I especially liked this one:

"Well Ashley was able to do this because this is not a multi period game. Ashley would have cooperated if this was a multi period game and there was a different way where other seven players could harm her (in a different game may be). There was an absence of threat which made it possible for her to cheat.

— Imad Qureshi"

Christopher said...

I love this article. I searched for hours to find an article dealing with game theory, but I was forced to move on after a couple hours of frustration. Great find.

Jayden made a great comment this post as well. It pinpoints an important component of game theory: self-interest. By limiting the $20 bill bid to only one round, it is in each of the eight parties' best interest to disregard the future and maximize benefits in the one round alone. While it is true that cooperating would create the maximum pool of benefit, the result of such cooperation isn't the Nash Equilibrium because it isn't the bid each party would make regardless of the others.

Instead it is the bid each party would make under complete cooperation. However, since this game was only one round long, it was in the best interest of each party fake cooperation and then act in self interest. Ashley understood the concept, and she took advantage. In game theory, we have to remember to hold all other factors constant (like emotions, effect of choices on future relationships, and the like).

Dr. Tufte said...

-1 on Christopher for grammatical errors.

Colin: it would be great if you could relate this to something in the text, or in real life. The commenters like the article, so this would've been a good one to expand on.

I do a similar thing in face-to-face classes. I have students bid on a dollar bill, with the catch that the two top bids have to pay, but only the top bid gets the dollar. The equilibrium is that the price of the dollar will go to infinity, although I usually cut it off sooner. This game is useful because it illustrates the sort of problem that firms involved in R&D go through when they are competing to get to a patent first.