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TOPIC: Applying bids to multi-item auctions

Applying bids to multi-item auctions 3 weeks 1 day ago #1

Forking a new thread from
truedungeon.com/forum?view=topic&defaultmenu=141&catid=584&id=250328&start=48#353987

Matthew Hayward wrote:

Wade Schwendemann wrote:

Matthew Hayward wrote:
Example. there are 32 PyPs:

A bids $100 on 17
B bids $105 on 17
C bids $5 on 32
D bids $105 on 1
E bids $75 on 4, and $90 on 3, $100 on 2, and $110 on 1
F bids $1000 on 2
G bids $55 on 8

Who is winning what and at what price? And why?


Ok, with E bidding on 10 different PyPs, I would sort it as this

All 32 will have been bid on

A wants 17, and is will to pay 100 apiece
B wants 17, and is willing to pay 105 apiece
If these were the only two bids, a would be leading 15 PyPs at 100, B would be leading 17 at 105


I agree with Wade, and I'll try to fill in the details of why.

Imagine a very faithful, very patient virtual assistant to whom you have given the instructions "Try to win 17 PYPs at the lowest price you can. Don't pay more than $105 each." This assistant uses that information to place actual bids for individual items on your behalf, one at a time. Every bidder has such an assistant, and the assistants do not share knowledge with each other.

In my opinion, the appropriate auction result is the one that is consistent with this model. Of course there are implementation shortcuts available (edit: here is the implementation shortcut ), but to see how the model works, let's walk through all the actual bids which result deterministically from the application of B's bid.

Initially A bids $0.25 on PYP#1-17:

PYP#1-17 A $0.25
PYP#18-32 $0

1. B bids $0.25 on PYP#18-32.

PYP#1-17 A $0.25
PYP#18-32 B $0.25

2. B still needs two more, so he bids $0.50 on PYP#1. But now A needs one more, so he takes over PYP#18 from B at $0.25 (first bidder wins ties).

PYP#1 B $0.50
PYP#2-18 A $0.25
PYP#19-32 B $0.25

3. B still needs two more, so he bids $0.50 on PYP#2. But now A needs one more, so he takes over PYP#19 from B at $0.25 (first bidder wins ties).

PYP#1-2 B $0.50
PYP#3-19 A $0.25
PYP#20-32 B $0.25

... skip a bit, Brother Maynard ...

16. B still needs two more, so he bids $0.50 on PYP#15. But now A needs one more, so he takes over PYP#32 from B at $0.25 (first bidder wins ties).

PYP#1-15 B $0.50
PYP#16-32 A $0.25

17. B still needs two more, so he bids $0.50 on PYP#16. But now A needs one more, so he takes over PYP#1 from B at $0.50 (first bidder wins ties).

PYP#1 A $0.50
PYP#2-16 B $0.50
PYP#17-32 A $0.25

... orangutans, breakfast cereals, ...

33. B still needs two more, so he bids $0.50 on PYP#32. But now A needs one more, so he takes over PYP#17 from B at $0.50 (first bidder wins ties).

PYP#1-17 A $0.50
PYP#18-32 B $0.50

Note that this state precisely matches step 1, but the price of every item has increased by one bid increment.

34. B still needs two more, so he bids $0.75 on PYP#1. But now A needs one more, so he takes over PYP#18 from B at $0.50 (first bidder wins ties).

PYP#1 B $0.75
PYP#2-18 A $0.50
PYP#19-32 B $0.50

35. B still needs two more, so he bids $0.75 on PYP#2. But now A needs one more, so he takes over PYP#19 from B at $0.50 (first bidder wins ties).

PYP#1-2 B $0.75
PYP#3-19 A $0.50
PYP#20-32 B $0.50

... lather, rinse, repeat ...

2849. B still needs two more, so he bids $100 on PYP#32. But now A needs one more, so he takes over PYP#17 from B at $100 (first bidder wins ties).

PYP#1-17 A $100
PYP#18-32 B $100

Note that this state precisely matches step 1, but the price of every item has increased by 89 bid increments. (If my arithmetic came out right.)

2850. B still needs two more, so he bids $105 on PYP#1. But now A needs one more, so he takes over PYP#18 from B at $100 (first bidder wins ties).

PYP#1 B $105
PYP#2-18 A $100
PYP#19-32 B $100

... almost there ...

2864. B still needs two more, so he bids $105 on PYP#15. But now A needs one more, so he takes over PYP#32 from B at $100 (first bidder wins ties).

PYP#1-15 B $105
PYP#16-32 A $100

2865. B still needs two more, so he bids $105 on PYP#16. At this point A has exhausted his maximum bid and does nothing further.

PYP#1-16 B $105
PYP#17-32 A $100

2866. B still needs one more, so he bids $105 on PYP#17.

PYP#1-17 B $105
PYP#18-32 A $100

B is now winning 17 PYPs, so he is satisfied and stops. A is paying $100 for 15 PYPs, which is fewer than he wanted but still within his acceptable parameters.

Note: had A only wanted 15 PYPs, he could have had them for $0.25 each back in step 3 (well, until other bidders came along). But because he wanted 17, his faithful assistant keeps bidding until either B gives up or A's max price is reached.

C bids, and doesnt take over any
D bids, and is now leading a PyP, leaving A with 14 at 100 and B with 17 at 105
E bids and is now leading 1 at 105 (with a max of 110), leaving A with 13 at 100, B and C unchanged.
F bids, taking control of 2, at 105 apiece (with a max of 1000), A now controls 11 at 100, B-E unchanged
G bids, nothing changes.


Agreed. Each of D, E, and F will bid on the cheapest available PYPs they can, taking them away from A (who is unwilling to go higher) by bidding one increment above the current price.

PYP#1-17 B $105
PYP#18 D $105
PYP#19 E $105
PYP#20-21 F $105
PYP#22-32 A $100

This is all because A and B combined wanted more than were available, so had to outbid one another. A's initial bid would have seen 17 PyP at $0.25, with 15 left at $0

If there were 34 PYPs available, the end result might look different.


Here's the problem I see with this:

A's price on the items A won depends in part on what A bid, rather than being completely determined by the bids of other bidders in your scenario. If A had bid $95 they would be paying $95 - right?


Yes, but everyone else who outbid A would be paying only $100 instead of $105:

PYP#1-17 B $100
PYP#18 D $100
PYP#19-21 E $100
PYP#22-23 F $100
PYP#24-32 A $95

and A is still winning fewer PYPs than he wanted. In particular, other people are winning PYPs that A wants for a price that A would have been willing to match (yet in this case chose not to bid).

(let's pretend E didn't have 2 bids at $100 to avoid what is ultimately an irrelevant complication that does not undermine this point)


It's relevant because including E's bids demonstrates the risk A takes by bidding less than he's actually willing to pay.

So, I would not be super happy in this scenario to be A, and to discover that the reason why I paid $100 a token, instead of $95 a token, was because I bid $100 instead of $95 - and I would have won the same number of tokens in either case.


The only way A would have won the same number of tokens is if nobody else bid $100. A can't possibly know this ahead of time, so he must make a choice and take a risk.

If anyone after A bids $100 (or if anyone before A bids $95), A wins more tokens by bidding $100. According to the instructions A gave his faithful assistant (try to win 17 PYPs for up to $100 each), winning more tokens is a better outcome.

If A would prefer the outcome of winning fewer tokens and spending less, he can bid differently: "assistant, try to win 7 PYPs for up to $100 each, or 17 PYPs if you can get them for only $90 each". In this example that yields

PYP#1-17 B $95
PYP#18 D $95
PYP#19-21 E $95
PYP#22-23 F $95
PYP#24-32 A $90

which means A wins 9 PYPs for $90 (instead of 11 for $100), because he stops trying to bid on a 10th one after the price gets above $90.

But for me, I'd want my auctions to have these properties:

A. The amount the winning bidders pay per item depends only on what other bidders bid, not what the winning bidder bid. (Of course the number of items a bidder wins depends on what they bid.)

This rules out the possibility of scenarios where:
* If a bidder had bid less, they would win the same items but pay less
* If a bidder had bid more, they would win the same items but pay more

This is true in an eBay style auction.


It's also true for the virtual-assistant model if all 32 PYPs are won by the same person. But you can't bid in 32 separate eBay auctions for individual PYPs and guarantee that you'll win at most 17 of them, unless you're prepared to do all your bidding manually (i.e. don't bid on a new 17th one until you see you've been outbid for one of the others).

B. The order in which bidders bid does not matter at all, with the exception that when two bidders bid the exact same amount priority is given to the earlier bidder in determining who gets the winning items.

This rules out the scenario where non-identical bids being re-ordered leads to a different result in any way, either in terms of price or who is winning what quantities.

It also rules out any scenario where a winning bidder pays a different amount if one re-ordered identical bids (although such a reordering might change how many items they win, it wouldn't change what they pay on the items they won).


I don't agree that this property is fundamentally desirable. In the virtual-assistant model, later bidders are obligated to actually outbid an earlier bidder for the same items, increasing the price by at least one bid increment:

PYP#1-17 B $105
PYP#18-32 A $100

whereas if B' had bid before A, he would only have to match but not exceed A's maximum price in order to win the desired 17 PYPs:

PYP#1-17 B' $100
PYP#18-32 A $100

This seems reasonable to me, and in keeping with our oft-stated intention to reward early bidding (which is valuable because it helps auctions succeed).

In my opinion the core "eBay style" property that's desirable for TD token auctions is the ability to privately input your maximum bid(s) one time, and have your actual bids automatically generated from that information on your behalf. The implementation is more complex for multi-item auctions than it is for single-item auctions, but I think the virtual-assistant conceptual model is clear and fair.

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Last edit: by David Zych. Reason: add link to implementation shortcut post

Applying bids to multi-item auctions 3 weeks 1 day ago #2

Well, naturally I agree with all of this.

I think there are a lot of different, fair ways to run an auction. As long as everyone knows what they're getting into up front, I'm good with it.
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Applying bids to multi-item auctions 3 weeks 1 day ago #3

Cheers to this. Though to be fair I had kinda just sorta assumed this was the standard way people ran these auctions and hadn't realized there was contention on how exactly they worked.

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Applying bids to multi-item auctions 3 weeks 1 day ago #4

Azzy wrote: Cheers to this. Though to be fair I had kinda just sorta assumed this was the standard way people ran these auctions and hadn't realized there was contention on how exactly they worked.


Well, normally there isnt a big issue; once enough bids come in, it all gets sorted out with all top bids close together. It became a discussion point on the recent auction because one of the first bids was for $105 on EVERY PYP. Then a few bids outbid at 110, and the next highest losing bid was 70. Meaning there were a few winners that were set to 110 so they could beat the 105, but the auction then listed the rest at 75 because that was the next competing bid.

So, it has to be a series of bids, else you have those 110 bidders pipe up "hey, screw my 110 bid, i will just bid 80 on one of those $75 PYPs.

So, it is really the first losing bid that sets the price. For 34 PYPs, it is bid 35 that sets it; every bid above it is set at one increment above, and any equal bids that came in before get it at that price.

Interestingly, this means that bidding on all or most of the tokens in a multi-item auction could push the price higher since as soon as one of your bids gets bumped off the list, it should become the first losing bid and set the current price across the board.
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Applying bids to multi-item auctions 3 weeks 1 day ago #5

David Zych wrote: Imagine a very faithful, very patient virtual assistant to whom you have given the instructions "Try to win 17 PYPs at the lowest price you can. Don't pay more than $105 each." This assistant uses that information to place actual bids for individual items on your behalf, one at a time. Every bidder has such an assistant, and the assistants do not share knowledge with each other.


This whole post seems super fun and I'll add more later, but I think it's important to add that the solution here is not only with the assistant side.

The auctioneer makes choices in how they run their auction. The auctioneer behavior influences your assistants ability to achieve "the lowest price you can." As an auctioneer I can create structures where people pay more or less for the same things with the same bids, and still have it be "the lowest price you can" within the given structure.

Here is one thing I would want my auctioneer to guarantee me:

1. The price I pay in no way depends on my max bid - it only depends on what other people's max bids are. (Of course the number of items I win can depend on my max bid).

This is important because the auctioneer has access all the sealed bids, and knows exactly what I'm willing to pay ($105 in this case). If this is not true there is an incentive for the auctioneer to structure the rules in a way that causes me to pay more than I would have otherwise based on their knowledge of my top dollar bid.

2. No one who bid less than me will receive an identical item to me at a lesser price.

This is important because my time is valuable and I don't want to have to reverse engineer a complex bidding system to know if this is true, and that perhaps I'm overpaying by not submitting my bids with a certain strategy. If someone can pay less than me by bidding less, it means I can't just fire in my top dollar price for these and come back later and be assured that I paid the least I could have given all other bids (as I can on eBay).


I also think it's important that very few people, if any, would actually rather have 17 PyPs at $105 each than 16 at $80. With the difference in cost they could buy a $250 pack from TD, get their 17th PyP, and have money to burn left over. So you should tell your minions to like, be more smart and not take you so literally ;).

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Last edit: by Matthew Hayward.

Applying bids to multi-item auctions 3 weeks 1 day ago #6

David Zych wrote: Forking a new thread from
truedungeon.com/forum?view=topic&defaultmenu=141&catid=584&id=250328&start=48#353987
I agree with Wade, and I'll try to fill in the details of why.

Imagine a very faithful, very patient virtual assistant to whom you have given the instructions "Try to win 17 PYPs at the lowest price you can. Don't pay more than $105 each." This assistant uses that information to place actual bids for individual items on your behalf, one at a time. Every bidder has such an assistant, and the assistants do not share knowledge with each other.

In my opinion, the appropriate auction result is the one that is consistent with this model. Of course there are implementation shortcuts available, but to see how the model works, let's walk through all the actual bids which result deterministically from the application of B's bid.

Initially A bids $0.25 on PYP#1-17:

PYP#1-17 A $0.25
PYP#18-32 $0

1. B bids $0.25 on PYP#18-32.

PYP#1-17 A $0.25
PYP#18-32 B $0.25

...snip...


I think what you're doing is equivalent to the short description in steps 1 and 2 below, can you check my logic on that?

Auction system proposed:

1. Take all the bid amounts and quantities, and at the end of the bidding period:

2. Run a serial (virtual) auction for each identical item sequentially, one at a time, using eBay rules. As bidders win these serial auctions, removing their winning bids from the bid pool at the start of the subsequent auction.

If this is equivalent to your approach, consider what happens in this scenario:

Auction House Alpha:
Auction house alpha follows the "serial virtual ebay auction" approach described above.

There are 2 identical items available.

A bids first and wants 1 item at $105 or less
B bids second and wants 1 item at $100 or less
C bids third wants 1 item at $1 or less

I think your system results in:

A wins an item for $100 + increment.
B wins an item for $1 + increment

To me it is obvious there is something wrong with this outcome: If A had bid $99 they would pay $1+increment - but because they bid $105 instead they paid $100+increment!

This absurd result comes about because this auction style allows the scenario where bidder A pays more for an identical item than bidder B, who has bid less than them.

The fact that "that probably won't happen" does not make this a good way to run an auction.

Now consider Auction House Beta:

Auction house beta runs their auctions this way (which is a common way to run multi-item auctions):

1. A bid is a ( $max amount, quantity ) pair.
2. All bids are sorted based on max amount, breaking ties on earliest bid submitted.
3. Winning items are awarded to bidders in the sorted order above, until all items are allocated.
4. The winning price is determined by the amount of the first bid that didn't win any items.

In the same scenario as Alpha house, e.g.:
There are 2 identical items available.

A bids first and wants 1 item at $105 or less
B bids second and wants 1 item at $100 or less
C bids third wants 1 item at $1 or less

The result is:
A wins an item for $1
B wins an item for $1


Which auction house will you tell your minions to go to?

I would send mine to Beta House.


I can understand why auctioneers want to run things the way Alpha house does - it generates more money for them. I don't understand why bidders would to go Alpha house.

What properties of an Alpha house auction do you value that are not also present in a Beta house auction?

For bidders, Beta House style auctions are guaranteed to have prices less than or equal to alpha house auctions for all winners. Any time Alpha House has prices that aren't all the same, Beta House would save some bidders money - and can never cost a bidder more than Alpha house. It is impossible for a winner at Alpha House to not also win the same quantity of items at Beta House (assuming Alpha house also breaks ties on the same bid by earliest bid).


I think I might try to run auctions of this kind when we get around to the 2020s. It will be funny when none of them hit their $7500 reserve limit due to not running up prices only on the bidders who were willing to pay more :laugh: .

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Last edit: by Matthew Hayward.

Applying bids to multi-item auctions 3 weeks 1 day ago #7

I dont know about the system that was proposed above, but my system is
A bids on item, takes the lead at 0.25
B is on item, takes the lead at 0.25
C bids on item, but at a max of $1

Since they bid first, A and B take the lead at $1 each, as they bid before C.

Basically, all winning bids are within one bid increment of one another.

If someone bids before you and has a lower max bid than you, they are the first ones to lose their items when your higher bid comes in.

If you want 10, and they want 5 of an item there are 12 of, shouldnt you have to pay more for the privilege of getting the number of items you want, and doing so later?

If you bid first with the higher max bid, you only pay their max bid for your items and get the number you want.

I'm not sure if I'm saying something very similar or something very different from what you're after. I am planning to try to figure out the difference between the final numbers for my recent auction using the method I described and what they would have been had I used your method.

I cannot guarantee I will get this done, but I am planning to try.
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Applying bids to multi-item auctions 3 weeks 1 day ago #8

Wade Schwendemann wrote: I dont know about the system that was proposed above, but my system is
A bids on item, takes the lead at 0.25
B is on item, takes the lead at 0.25
C bids on item, but at a max of $1

Since they bid first, A and B take the lead at $1 each, as they bid before C.

Basically, all winning bids are within one bid increment of one another.

If someone bids before you and has a lower max bid than you, they are the first ones to lose their items when your higher bid comes in.

If you want 10, and they want 5 of an item there are 12 of, shouldnt you have to pay more for the privilege of getting the number of items you want, and doing so later?

If you bid first with the higher max bid, you only pay their max bid for your items and get the number you want.

I'm not sure if I'm saying something very similar or something very different from what you're after. I am planning to try to figure out the difference between the final numbers for my recent auction using the method I described and what they would have been had I used your method.

I cannot guarantee I will get this done, but I am planning to try.



Hmm. What do you do in this scenario:

S1
3 identical items
A wants 2 at $105
B wants 2 at $100
C wants 1 at $1

And this one:

S2
3 identical items
A wants 2 at $105
B wants 1 at $100
C wants 1 at $1

In both scenarios my approach gives A two items, B one item, and both A and B pay $1.

I suspect deviating from my approach gives a large difference in the cost someone pays between S1 and S2.

I suspect this deviation would cause bidders to prefer my approach.

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Applying bids to multi-item auctions 3 weeks 1 day ago #9

Matthew Hayward wrote:

Wade Schwendemann wrote: I dont know about the system that was proposed above, but my system is
A bids on item, takes the lead at 0.25
B is on item, takes the lead at 0.25
C bids on item, but at a max of $1

Since they bid first, A and B take the lead at $1 each, as they bid before C.

Basically, all winning bids are within one bid increment of one another.

If someone bids before you and has a lower max bid than you, they are the first ones to lose their items when your higher bid comes in.

If you want 10, and they want 5 of an item there are 12 of, shouldnt you have to pay more for the privilege of getting the number of items you want, and doing so later?

If you bid first with the higher max bid, you only pay their max bid for your items and get the number you want.

I'm not sure if I'm saying something very similar or something very different from what you're after. I am planning to try to figure out the difference between the final numbers for my recent auction using the method I described and what they would have been had I used your method.

I cannot guarantee I will get this done, but I am planning to try.



Hmm. What do you do in this scenario:

S1
3 identical items
A wants 2 at $105
B wants 2 at $100
C wants 1 at $1

And this one:

S2
3 identical items
A wants 2 at $105
B wants 1 at $100
C wants 1 at $1

In both scenarios my approach gives A two items, B one item, and both A and B pay $1.

I suspect deviating from my approach gives a large difference in the cost someone pays between S1 and S2.

I suspect this deviation would cause bidders to prefer my approach.


You are correct.

S1
A gets the 2 items they want, and pays $100
B gets 1 of the 2, and pays $100
C gets nothing

S2
A gets 2 items for $1
B gets 1 item for $1
C gets nothing

I believe that, while the result is the same with your method between the 2, the difference lies in the desires of the bidders.

Their desires need to be respected and accounted for in some way.
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Applying bids to multi-item auctions 3 weeks 1 day ago #10

Matthew Hayward wrote: Hmm. What do you do in this scenario:

S1
3 identical items
A wants 2 at $105
B wants 2 at $100
C wants 1 at $1

And this one:

S2
3 identical items
A wants 2 at $105
B wants 1 at $100
C wants 1 at $1

In both scenarios my approach gives A two items, B one item, and both A and B pay $1.

I suspect deviating from my approach gives a large difference in the cost someone pays between S1 and S2.

I suspect this deviation would cause bidders to prefer my approach.


In S1, I believe A has 2 @ $100 and B has 1 @ $100. How does your approach allow B to be happy about not getting his 2nd item in scenario 1?

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Applying bids to multi-item auctions 3 weeks 1 day ago #11

Lequinian wrote:

Matthew Hayward wrote: Hmm. What do you do in this scenario:

S1
3 identical items
A wants 2 at $105
B wants 2 at $100
C wants 1 at $1

And this one:

S2
3 identical items
A wants 2 at $105
B wants 1 at $100
C wants 1 at $1

In both scenarios my approach gives A two items, B one item, and both A and B pay $1.

I suspect deviating from my approach gives a large difference in the cost someone pays between S1 and S2.

I suspect this deviation would cause bidders to prefer my approach.


In S1, I believe A has 2 @ $100 and B has 1 @ $100. How does your approach allow B to be happy about not getting his 2nd item in scenario 1?


Probably because he only has to pay $1 for the one he does get!

It's a different way of looking at it.

I'm enjoying this exercise, but it definitely does show different priorities.

In this example, were I B, I might wonder why I didnt get 2 items. If the bid were at my max, I would know that I lost because A bid first without having to ask.
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Applying bids to multi-item auctions 3 weeks 1 day ago #12

Wade Schwendemann wrote:

Matthew Hayward wrote:

Wade Schwendemann wrote: I dont know about the system that was proposed above, but my system is
A bids on item, takes the lead at 0.25
B is on item, takes the lead at 0.25
C bids on item, but at a max of $1

Since they bid first, A and B take the lead at $1 each, as they bid before C.

Basically, all winning bids are within one bid increment of one another.

If someone bids before you and has a lower max bid than you, they are the first ones to lose their items when your higher bid comes in.

If you want 10, and they want 5 of an item there are 12 of, shouldnt you have to pay more for the privilege of getting the number of items you want, and doing so later?

If you bid first with the higher max bid, you only pay their max bid for your items and get the number you want.

I'm not sure if I'm saying something very similar or something very different from what you're after. I am planning to try to figure out the difference between the final numbers for my recent auction using the method I described and what they would have been had I used your method.

I cannot guarantee I will get this done, but I am planning to try.



Hmm. What do you do in this scenario:

S1
3 identical items
A wants 2 at $105
B wants 2 at $100
C wants 1 at $1

And this one:

S2
3 identical items
A wants 2 at $105
B wants 1 at $100
C wants 1 at $1

In both scenarios my approach gives A two items, B one item, and both A and B pay $1.

I suspect deviating from my approach gives a large difference in the cost someone pays between S1 and S2.

I suspect this deviation would cause bidders to prefer my approach.


You are correct.

S1
A gets the 2 items they want, and pays $100
B gets 1 of the 2, and pays $100
C gets nothing

S2
A gets 2 items for $1
B gets 1 item for $1
C gets nothing

I believe that, while the result is the same with your method between the 2, the difference lies in the desires of the bidders.

Their desires need to be respected and accounted for in some way.


Hold on, i think i missed something. What method has S1 result in A getting two, B getting one, and all 3 sell for $1? Because that should be right out. If i am B, i would call bullshit. I wanted a 2nd item, and i bid more than the $1 selling price.
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