Dollar–Bill Auctions
The article introduces the dollar‐bill auction as an “unpleasant economists’ party
game” that was invented by the game theorist Martin Shubik. As the name
suggests, the participants’ agree to auction one-dollar by placing bids, with one-cent increments. Just like a normal auction, the one-dollar bill goes to the highest
bidder, but what makes this auction interesting is that both the highest and
second-highest bidder has to pay.
As the article mentions, bids quickly rise close to a dollar and we reach a point
where the highest-bidder has bid 99 cents, and the “under-bidder” has bid 98
cents. The “under-bidder” is better off to increase his bid to a dollar and try to
win – since that is better than losing 98 cents.
Will the bid stop at one dollar? No!
Now the new “under-bidder” is in a position to lose 99 cents. However, note that
if he bids 1.01 dollars and wins he could reduce his possible loss from 99 cents to
just 1 cent. So the under-bidder always bounces back, and the auction will
continue until the players use up all their resources. In the case, one might not
want to take part in the auction at all, but that would lead to having a one-dollar
bill for taking! Shubik believed that the above was a paradox to which game
theory had no solution.
So what’s the best way out then? “Avoid situations which mimic the structure of
this game”. But is it really that easy to avoid such situations?
Unfortunately, it’s not that easy to avoid this. The crux of this problem is that
people always feel that they will be better off if they spend a bit more and
avoid a greater loss. The author highlights several real-world political/economic
scenarios where this principle is pertinent. A few of his examples are as follows:
- It is definitely better to write off Greece’s debt obligations, even to the
extent writing off the entire Greek economy for the sake of sustaining the
European economic integration. - Similarly, bearing the costs to rescue Lehman during financial crisis
would have been far more preferable than bearing the costs of a global
financial economy collapse. - We have situations where we give into demands of hijackers to save more
precious lives of humans. - It’s always better to spend a bit more to complete a large-scale project that
has already exceeded the budget than to keep it incomplete.
Talking specifically about the Greek economic crisis, the author expresses
his opinion that the U.S. is in fact in a situation similar to a dollar-bid
auction and must do whatever it can for the sake of keeping the European
unity intact, and thus must stay in the auction for as long as it takes for
achieving the above.
It’s interesting to note that the winner in a dollar-bid auction sacrifices
bears a large cost to win the dollar-bill. Factually, both the highest bidder
and the second highest bidder lose, but the relative winner is who stays
the longest. Thus interestingly, in this case the winner is not always the
person who is rational. This is unusual and different from second‐price
auctions mentioned in class where one’s dominant strategy is to always
bid one’s true value and thus in a sense stay “rational”.
Relevance to Class: The above‐mentioned concepts relate to the class discussion
on Auctions (Chapter 9) and a bit on Game Theory (Chapter 6). It explores what
is the best bidding strategy for a person in a dollar-bid auction and analyzes the
various payoffs for each of his actions. Unlike second-price auctions where
bidding one’s true value is the dominant strategy, we learn how that is not
always the case for dollar‐bill auctions where being irrational and staying longer
might have a greater payoff.
Reference/Source:
http://www.johnkay.com/2011/07/27/kipling%E2%80%99s-game-theory-lessons-for-greece