How to sell a dollar for more than a dollar

In this time of cutbacks and furloughs professors need a quick source of extra cash.  David Zetland explains how to sell a dollar for more than a dollar (and teach some game theory and something about political lobbying at the same time). 


I do this in class, but I use a $20 bill. That seems to work better.

The Prisoner's Dilemma is a better analogy for political lobbying or arms races, where the optimal move is to help yourself which indirectly harms others.

In this game, the optimal strategy is not to bid or bid exactly a dollar. We don't think that all lobbying is bad for the lobbyists themselves, which would have to be the case for this to be a good analogy.


Bill: we should be so lucky!

Actually, I think that this model works very well. Of course there are some major differences.

In practice, there are often two bidders: someone wants a bid, and someone does not. This means that the bids are cumulative, which this exercise misses. (A bids 1,3,5 while F bids 2,4,6. Total bidding is 11, not 21.)

Note that this example can get even more interesting in this case, as the bids might well run .7, .8, .9, 1.0, 1.1, 1.2.... Where each bidder is only adding .2 to their bid to gain 1.

Second, despite the fact that these are modern times, politicians tend to be very much bought rather than rented. Just from the title of a bill, I would expect that we can predict the results for individual congressmen to 80% or better. Since the bids are more for a term of control of a seat, rather than an individual bill, the total amount of money to be had is in fact flexible.

This is a great, classic example for students, but I thought the instructor here did a very awkward job.

I always loved this game theory example, and came across it first through dinosaur comics a few weeks ago. I would recommend if you want a more in depth analysis of the game.


No, the first bidder should bid a dollar. If you bid .99, I might get some spite benefit, and bid a dollar, but I would be uncertain that you would not want to do the same to me. Safer not to bid or to bid true value as first bidder as dominant strategy.

I do this in class, but start with 5 or 10 cent increments. it really highlights the difference between the Marginal Cost, and the Cost already incurred (sunk cost as noted). Marginal Cost being the bid, and the Marginal Benefit (the chance to win the dollar, and if there are only a couple people bidding - as is most often the case- the chance to win is pretty good, making the MB = chance * $1 > MC)

Rational to keep bidding. Starting to Bid is unwise though, unless there is significant enjoyment from the thrill of the bid (i sold one a few years ago for $8).

I found this to be extremely interesting, and I completely agree that no one wins in this scenario except for the person putting the dollar up for bid. I mean how fast did the bidders perceptions change from trying to make a profit to trying to minimize losses. It truly makes me wonder just how far will lobbyists will go to try and get their version of a law passed. Because it seems as though the lobbyists spending will exponentially increase until one finally backs down or until they bankrupt themselves. It's no wonder many politicians these days seem to be out of touch with the people when lobbyists are getting into competitions like this over their favor.

fuwen 2010.03.23

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