From: positron@engin.umich.edu (Jonathan Scott Haas)
Subject: Re: Politics Game
Date: Fri, 13 Nov 92 16:10:18 EST
Organization: University of Michigan Engineering, Ann Arbor

In article <Z_C=4G+@engin.umich.edu> positron@engin.umich.edu (Jonathan Scott Haas) writes:
>
>This sounds a lot like the "Dollar Bill Auction" described by William
>Poundstone in his book, "Prisoner's Dilemma".
>

I've received a request to post the rules for this, so here they are. This
is typed in without permission from Poundstone's book, but I don't think
he'd mind.

...
  [Martin] Shubik posed the question of whether it was possible to incorporate
*addiction* in a game. This question lead to the dollar auction. Shubik is
uncertain who thought of the game first or whether it was a collaboration.
In any case, Shubik published it in 1971 and is generally credited as the
game's inventor.

  In his 1971 paper, Shubik describes the dollar auction as an "extremely
simple, highly amusing and instructive parlor game." A dollar bill is 
auctioned with these two rules:
  1. (As in any auction) the dollar bill goes to the highest bidder, who
pays whatever the high bid was. Each new bid has to be higher than the
current high bid, and the game ends when there is no new bid within a
specified time limit.
  2. (Unlike at Sotheby's!) the *second-highest* bidder also has to pay
the amount of his last bid--and gets *nothing* in return. You really
don't want to be the second-highest bidder.

  Shubik wrote, "A large crowd is desirable. Furthermore, experience has
indicated that the best time is during a party when spirits are high and
the propensity to calculate does not settle in until at least two bids
have been made."

  Shubik's two rules swiftly lead to madness. "Do I hear 10 cents?" asks
the auctioneer--"5 cents?"

  Well, it's a dollar bill, and anyone can have it for a penny. So someone
says 1 cent. The auctioneer accepts the bid. Now anyone can have the
dollar bill for 2 cents. That's still better than the rate Chase Manhattan
gives you, so someone says 2 cents. It would be crazy not to.

  The second bid puts the first bidder in the uncomfortable position of
being the second-highest bidder. Should the bidding stop now, he would be
charged 1 cent for nothing. So this person has particular reason to make
a new bid--"3 cents." And so on...

  Maybe you're way ahead of me. You might think that the bill will finally
go for the full price of $1.00--a sad comment on greed, that no one got a
bargain. If so, you'd be way too optimistic.

  Eventually someone does bid $1.00. That leaves someone else with a
second-highest bid of 99 cents or less. If the bidding stops at $1.00,
the underbidder is in the hole for as much as 99 cents. So this person
has incentive to bid $1.01 for the dollar bill. Provided he wins, he would
be out only a penny (for paying $1.01 for a dollar bill). That's better
than losing 99 cents.

  That leads the $1.00 bidder to top *that* bid. Shubik wrote, "There is a
pause and hesitation in the group as the bid goes through the one dollar
barrier. From then on, there is a duel with bursts of speed until tension
builds, bidding then slows and finally peters out."

  No matter what the stage of the bidding, the second-highest bidder can
improve his position by almost a dollar by barely topping the current
high bid. Yet the predicament of the second-highest bidder gets worse
and worse! This peculiar game leads to a bad case of buyer's remorse.
The highest bidder pays far more than a dollar for a dollar, and the second-
highest bidder pays for more than a dollar for *nothing*.

[rest of section omitted]


-- 
__/\__  Jonathan S. Haas         | Jake liked his women the way he liked
\    /  University of Michigan   | his kiwi fruit: sweet yet tart, firm-
/_  _\  positron@engin.umich.edu | fleshed yet yielding to the touch, and
  \/                             | covered with short brown fuzzy hair.