Though I have not read it completely as yet, here's an interesting parable I wish to share:
How to auction a $1 bill for more than it's worth:
This is a story about a professor at Yale. He routinely used to auction $1 bills in his class. But the rules were a little different - while the highest bidder gets the bill, the second highest bidder will also have to pay. The increments are allowed a minimum of 5 cents.
So, the incentive is clear: You can bid sufficiently lower than $1 and still get the bill. Assume the highest bid at some point is 40 cents (A) and the second highest is 35 cents (B). Now, B has an apparent double incentive to bid at 45 cents - he needn't pay the 35 cents and he gets to keep the bill at 45 cents, albeit at a higher price than he earlier intended. Similar reasoning holds true for A. So, both A and B are now 'locked' into the auction - the 'double incentive' pushes the bid higher and higher. When B bids 1 $ and A is at 95 cents, A can bid at 105 cents and make a loss of 5 cents OR lose 95 cents. In this way, the $1 bill can be auctioned at much more than it's worth.
Interestingly, the auction grows from a 'maximise profit' to 'minimise loss' model.
13 comments:
There is an escape route out of this situation.
Although; it needs both the bidders to be smart enough to form a cartel and even then; the professor ends up in profit.
If A bids 'x cents', and B bids 'x cents + 1 dollar'. The loss / profit for both bidders is then same. So, although the locked situation is broken; The professor still gets at least 1 dollar ( assuming x = 0 ).
This reminds me of another puzzle : A professor asks the students to select any integer from 1 to 100. And offers the $1 prize to whoever selects the 2nd largest number.
hi funda...but the comment was cooler..lol
Lend me the book once you are done :)
@ Sumedh,
Yes, if they form a cartel, then the point is lost. In this case, since the bids should be multiples of 5 cents - a cartel can ensure that the prof. makes a loss. A bids 45, B bids 50. They close it there. Prof. loses 50, A and B share the loot.
@ Aroused - Thx.
@ IDR, Sure.
Actually the prof loses 5 cents. But then again, why would B share the $1 with A as he would get only 50 cents assuming equal sharing which essentially translates into no net profit for him. In this case, only A stands to gain (of 5 cents). So an alliance wouldn't really help. They as you rightly pointed out will be locked into the auction
Lays, you ought to take a course on game theory or read up that stuff... if the bidders are intelligent enough, the first one will bid $1 at the outset knowing the following:
1. If he bids anything more, he obviously makes a loss.
2. If he bids anything less, the second bidder will bid $1 and first one either has to raise the bid (thus getting the first bidder a loss) or give up (thus losing the money he had already bid). So if the first bidder does anything other than bid $1, he makes a loss.
Now, when the second bidder's chance comes, he will drop out - because if he raises the bids, he loses the amount by which he has raised. It is not in his interest to lose money to win the bid. And he can't bid anything less. Thus, the only way he has left to not to make a loss is to drop out of the bid.
Thus the best strategy from the bidders is for the first one to bid $1 and the second one to drop out - which results in nothing... no profits no losses for any of the prof/ bidders.
There is this auction site ( I think its Indian) which uses a similar but slightly different funda. You pay some small amount (say 5 cents) for every bid.
Google for it. I heard they were making decent profits.
-
Wiper
www.swoopo.com
http://en.wikipedia.org/wiki/Swoopo
@ Shounak, Yep.
@ Anurag - Interesting illustration there. Btw, who offers courses on Game theory in the insti?
@ Wiper - Swoopo is a fundoo concept. I especially loved the way the wiki page describes it "eBay's (more) evil cousin." ha ha
It is a great business plan none the less.
not sure... but someone in DoMS or CSE should be doing that
Why should A and B even bid 40 cents?
If they do form a cartel, and A and B bid some low amount and A 'pays off' B his full amount, then the prof will always be in a loss.
Is this somewhat similar to all the Nash equilibrium fundaes?
If minimising loss is the objective, and assuming all bidders are sufficiently intelligent, the optimal and ideal solution would be for no one to make any bids. You cannot minimise loss below 0 cents. Right?
Anyways, pass its the book. Save me the trouble of walking the 5 metres to your doorstep :)
http://www.scribd.com/doc/2067543/A-Mathematician-Plays-the-Stock-Market
That's a link to the book online. Pirated, yes. Direct download, yes. Free? Yes! win-win
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