Game Theory problem - Lowest Unique Bid Wins

[Dale Dough]

OK so in my idle hours I ran across this site. Before you get excited, I think this particular site is a scam (check T&C, it has the string [insert company name] somewhere).

The premise is interesting though, and I did find more legit looking sites auctioning off smaller items. I got excited and thought 'free moniez!', but then I thought some more. Here's the idea:

A townhouse worth $400k is auctioned off. The lowest unique bidder wins. So if two people bid $.01, one bids $.02, and two bid $.03, the 2 cent wins. You can bid as many times as you like, but it costs money to place a bid. In this case, let's say it costs $4. Bids are in 1 cent increments. In the unlikely event that there are no unique bids, the first bidder of the lowest amount with only two bids wins. Etc., etc.

There are many possible variations, but let's say this auction ends when 1 million bids are made, or after a certain amount of time. Also, information is limited. Once you make a bid, you either get no information, you get to know whether your bid is the current winner, and possibly a general idea of an upper bound bid. Also, in this particular case, the maximum bid is $10k.

Obviously you don't want to make more than 100 thousand bids - at least not a priori. Also, since there is an upper limit on the total number of bids, you'd be stupid to bid more than 5k - you'll be almost guaranteed to lose, and if you CAN win, a lower bid would have done the trick.

Obviously the game is massively -EV for the player base as a whole. But is it impossible to somehow Sklansky-profit from this - especially if you don't know how many bids have already been made? What if there is no maximum on the amount of bids, but only a time limit?

How would a (large) group of rational agents play this? How -EV is any particular bid? On one hand, higher numbers should have lower EV, because the higher you go the more likely it becomes that someone was the only one to pick a lower number. But going for 1c also seems kind of ridiculous. Unless of course everybody feels that way.. but there HAS to be a way to quantify this, right? Optimal strategy given an approximate number of opponents? Does it matter if you have 100 opponents or a million, given that each can afford to spend at least $399,999 if they have to?

This thing is giving me major headaches. FWIW, I did some more Googling and found similar, more trustworthy looking sites with Xboxes etc. going for like a dollar. There HAS to be +EV to be had here, right? Or is it just a clever variant of a lottery?

[ChrisV]

Hi,

This is called a Unique Bid Auction. There's some links to academic research on the subject at the bottom of the Wiki page.

If you aren't limited in the number of bids you can make, the ideal strategy is simple. You just make every single bid in between the minimum bid and the maximum you are willing to pay. This assures you of winning the item at the lowest possible price if it falls within the range you are willing to pay.

If you're limited in some way in the number of bids you can make, calculating the strategy with the best EV would involve knowledge of a few factors - the approximate market value of the item, the number of bids you'll be up against, and the statistical bidding tendencies of opponents, which I think would have to be determined experimentally. There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[doucy]

[ QUOTE ]
There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[/ QUOTE ]

No no, that's the jason_t dilemma

[Dale Dough]

Yeah, so it's a sucker's game.

I was browsing various 'auction' sites, and, much to my surprise, found one where it was possible to guarantee a win for less money than even the resale value of the item. I'm not going to go into specifics because it's still possible to somehow miraculously profit, but I very much doubt that I will.

There was a limit on the maximum number of bids. Say a thousand. Each bid costs $10, and the value of the item is 8k. The bid amount is negligible - 1c increments.

Theoretically, you can profit by bidding 501 times, covering every bid between $.01 and $5.01. One of the bids is guaranteed to be the lowest unique one, so you end up paying 5k and change for an 8k item. I'm slightly embarrassed to admit that I felt really smart when I figured that out and was ready to ship the dough then and there.

The problem is that if the auction doesn't close for several months, the fine print says they will cancel it and ship a 'proportionate' cash equivalent to the winner. If that happens, best case scenario you get 4k.

This is very likely to happen, since anyone with half a brain will realize that once 501 bids are made, it's very likely impossible to win. Especially if the bids were all made simultaneously - which you have to do, or you risk someone else beating you to it.

Of course, you can wait until a sufficient number of bids have been made and THEN bid 501 times, but people would be dumb to make those bids and leave themselves exposed. Or you could say [censored] it and bid anyway, and then hope enough people are stupid enough to waste their money on worthless bids.

So basically, you're gambling that enough people are dumb enough to make a bet they can never win - at least in the case of this particular auction.

In the case of the particular gem I found, I need two hundred more people to bid. If that happens, my potential profits start at a whopping $0 minus transfer fees, and everything else is gravy! Provided that the site isn't scamming us, of course. That, and I'll have to part with the money for a few months first. So far, a few weeks after the 'auction' started, we have... two bidders!

[OrigamiSensei]

[ QUOTE ]
There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[/ QUOTE ]
One reason why game theory fails in those cases is because some people instinctively recognize that going for the last incremental dollar just isn't as important as ensuring a near-maximal payout. It also fails to recognize the value of vengeance in such a scenario. If I can rely on my fellow passenger to realize that claiming $100 is not only a way to attain a near-maximal payout, it's also a way to guarantee collectively that the airline suffers the maximum overall ill effect for losing our luggage then the choice becomes easy.

A related problem is one where a person is given $1000 dollars. They are told they can choose how to split it with another person but if the other person rejects the split, both get nothing. Game theorists will spend lots of time trying to figure out probability ratios for squeezing out extra amounts of money over $500. Meanwhile, fair-minded people will instinctively and quickly offer a 50/50 split as being a solution that will make both parties happy and have a vanishingly low chance of getting rejected. It's "bad" in game theory but in real life it's called a win-win and it makes life a lot easier in the long run. It certainly helps to eliminate the what-ifs of a situation gone bad.

[ChrisV]

[ QUOTE ]
[ QUOTE ]
There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[/ QUOTE ]
One reason why game theory fails in those cases is because some people instinctively recognize that going for the last incremental dollar just isn't as important as ensuring a near-maximal payout. It also fails to recognize the value of vengeance in such a scenario. If I can rely on my fellow passenger to realize that claiming $100 is not only a way to attain a near-maximal payout, it's also a way to guarantee collectively that the airline suffers the maximum overall ill effect for losing our luggage then the choice becomes easy.

[/ QUOTE ]

Peoples' behavior will be the same if the vengeance aspect is not present. When this problem was tested experimentally, it wasn't present and people still tended towards higher amounts.

The problem with the game theory solution here isn't that people don't actually do it, because that wouldn't matter if the game theory solution was better. It's that the game theory answer really is wrong, because it is aiming at the wrong goal (getting the largest payoff every time, rather than maximising EV)

[ QUOTE ]
A related problem is one where a person is given $1000 dollars. They are told they can choose how to split it with another person but if the other person rejects the split, both get nothing. Game theorists will spend lots of time trying to figure out probability ratios for squeezing out extra amounts of money over $500. Meanwhile, fair-minded people will instinctively and quickly offer a 50/50 split as being a solution that will make both parties happy and have a vanishingly low chance of getting rejected. It's "bad" in game theory but in real life it's called a win-win and it makes life a lot easier in the long run. It certainly helps to eliminate the what-ifs of a situation gone bad.

[/ QUOTE ]

One problem is that what is being split isn't money but utility. If the money was $100,000 I was up against some busto guy, I might (if I felt like being a jerk) split it 70/30 or something, confident that he wouldn't reject. If I was up against Bill Gates, I wouldn't be trying the same trick.

[ALawPoker]

Market efficiency strikes again.

[Duke]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[/ QUOTE ]
One reason why game theory fails in those cases is because some people instinctively recognize that going for the last incremental dollar just isn't as important as ensuring a near-maximal payout. It also fails to recognize the value of vengeance in such a scenario. If I can rely on my fellow passenger to realize that claiming $100 is not only a way to attain a near-maximal payout, it's also a way to guarantee collectively that the airline suffers the maximum overall ill effect for losing our luggage then the choice becomes easy.

[/ QUOTE ]

Peoples' behavior will be the same if the vengeance aspect is not present. When this problem was tested experimentally, it wasn't present and people still tended towards higher amounts.

The problem with the game theory solution here isn't that people don't actually do it, because that wouldn't matter if the game theory solution was better. It's that the game theory answer really is wrong, because it is aiming at the wrong goal (getting the largest payoff every time, rather than maximising EV)

[ QUOTE ]
A related problem is one where a person is given $1000 dollars. They are told they can choose how to split it with another person but if the other person rejects the split, both get nothing. Game theorists will spend lots of time trying to figure out probability ratios for squeezing out extra amounts of money over $500. Meanwhile, fair-minded people will instinctively and quickly offer a 50/50 split as being a solution that will make both parties happy and have a vanishingly low chance of getting rejected. It's "bad" in game theory but in real life it's called a win-win and it makes life a lot easier in the long run. It certainly helps to eliminate the what-ifs of a situation gone bad.

[/ QUOTE ]

One problem is that what is being split isn't money but utility. If the money was $100,000 I was up against some busto guy, I might (if I felt like being a jerk) split it 70/30 or something, confident that he wouldn't reject. If I was up against Bill Gates, I wouldn't be trying the same trick.

[/ QUOTE ]

Yeah I'd rather get zero than 49,999 to the other guy's 50,001. It's a matter of principle.

I'd offer a homeless crack head the same $50k as I offered Bill Gates.

[xSCWx]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
There are many games where peoples' behaviour cannot be predicted via game theory; the Traveler's Dilemma problem, for instance.

[/ QUOTE ]
One reason why game theory fails in those cases is because some people instinctively recognize that going for the last incremental dollar just isn't as important as ensuring a near-maximal payout. It also fails to recognize the value of vengeance in such a scenario. If I can rely on my fellow passenger to realize that claiming $100 is not only a way to attain a near-maximal payout, it's also a way to guarantee collectively that the airline suffers the maximum overall ill effect for losing our luggage then the choice becomes easy.

[/ QUOTE ]

Peoples' behavior will be the same if the vengeance aspect is not present. When this problem was tested experimentally, it wasn't present and people still tended towards higher amounts.

The problem with the game theory solution here isn't that people don't actually do it, because that wouldn't matter if the game theory solution was better. It's that the game theory answer really is wrong, because it is aiming at the wrong goal (getting the largest payoff every time, rather than maximising EV)

[ QUOTE ]
A related problem is one where a person is given $1000 dollars. They are told they can choose how to split it with another person but if the other person rejects the split, both get nothing. Game theorists will spend lots of time trying to figure out probability ratios for squeezing out extra amounts of money over $500. Meanwhile, fair-minded people will instinctively and quickly offer a 50/50 split as being a solution that will make both parties happy and have a vanishingly low chance of getting rejected. It's "bad" in game theory but in real life it's called a win-win and it makes life a lot easier in the long run. It certainly helps to eliminate the what-ifs of a situation gone bad.

[/ QUOTE ]

One problem is that what is being split isn't money but utility. If the money was $100,000 I was up against some busto guy, I might (if I felt like being a jerk) split it 70/30 or something, confident that he wouldn't reject. If I was up against Bill Gates, I wouldn't be trying the same trick.

[/ QUOTE ]

Yeah I'd rather get zero than 49,999 to the other guy's 50,001. It's a matter of principle.

I'd offer a homeless crack head the same $50k as I offered Bill Gates.

[/ QUOTE ]

If you rejected 49,999 from me to my 50,001 money would be the least of your concerns.

[Dale Dough]

Reminds me of this story I've read on 2+2 somewhere.. some guy is pissing off some other guy at the poker table. Then the other (rich) guy shows quads over quads/top boat or sth and throws it in the much, purposely causing the first guy to miss out on the bad beat jackpot. I so hope that really happened...