David Zych wrote:
Matthew Hayward wrote:
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...
Here is what I think you're doing, is equivalent to can you tell me if it amounts to the same thing?
1. Take all the bid amounts and quantities, and at the end of the bidding period:
2. Run a virtual auction for each identical item sequentially, one at a time, using eBay rules, removing the winning bids from the bid pool at the start of the subsequent auction.
That's definitely not what I'm doing. I am running all 32 auctions at the same time, so that each virtual assistant can place its next actual bid on whichever item happens to be going for cheapest at that moment. None of the auctions is over until all virtual assistants have stopped bidding.
If so, consider what happens in this scenario:
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
Great example! Much easier to follow than 32 items.
Here's the step by step breakdown at Auction House Lambda:
1. A bids $0.25 on item 1. A is happy.
2. B bids $0.25 on item 2. B is happy.
At this point A and B are winning one item each for $0.25
3. C bids $0.50 on item 1 (outbidding A).
4. A bids $0.25 on item 2 (displacing B, since early bids win ties).
5. B bids $0.50 on item 2 (outbidding A).
6. A bids $0.50 on item 1 (displacing C, since early bids win ties).
At this point A and B are winning one item each for $0.50
7. C bids $0.75 on item 1 (outbidding A).
8. A bids $0.50 on item 2 (displacing B, since early bids win ties).
9. B bids $0.75 on item 2 (outbidding A).
10. A bids $0.75 on item 1 (displacing C, since early bids win ties).
At this point A and B are winning one item each for $0.75
11. C bids $1 on item 1 (outbidding A).
12. A bids $0.75 on item 2 (displacing B, since early bids win ties).
13. B bids $1 on item 2 (outbidding A).
14. A bids $1 on item 1 (displacing C, since early bids win ties).
At this point A and B are winning one item each for $1.
15. C gives up. A and B win for $1 each.
Hopefully this helps you see my conceptual model. You'll notice that in this simple case, Auction House Lambda and Auction House Beta end up with the same answer.
Yup - now I understand - I have an updated example that shows the problem with Lambda House below (it's already been mentioned in this thread in regard to some other systems).
Now suppose D wants one item at $110. At Auction House Lambda, D will bid both A and B up to $100, one increment at a time (just like C did), then bid $105 on item 1 (outbidding A). A bids $100 on item 2 (displacing B ), and B gives up.
Result: D wins for $105 and A wins for $100.
Auction House Beta would knock D's price down to $100 as well. That's good news (at least in the short term) if you're D. But I see three comparative downsides:
First, if I'm B, this result doesn't sit quite right. Shouldn't somebody who bids after me need to actually pay more than I was willing to pay in order to win the item I wanted?
No! They only need to
bid more than you - not
pay more than you.
If you're a bidder you'd appreciate that you could just as easily be A, B, or D in this auction- and look for an auction house which offers the best result no matter who you are (e.g. there's no reason to assume "you" are B - you might also be A, or D):
Lambda House:
A - Wins 1 token for $100
B - Wins 0 tokens.
D - Wins 1 token for $105
Beta House:
A - Wins 1 token for $100
B - Wins 0 tokens.
D - Wins 1 token for $100.
There is no difference if you're A or B, but D does better in Beta House. Since you don't know if you'll be bidder A, or B, or D when you place your bid, and since Beta House guarantees that :
i. You'll always win the quantity that you would have won at Lamdba House.
ii. You'll never pay more, and sometimes pay less than you would at Lambda House.
You would be wise to pick Beta house if your goal is to minimize your spend (again - no matter which house you choose you win the same number of items).
That's not a deal-breaker as long as the rules were stated clearly up front, but IMO it's a consideration.
This is pretty funny to me - as the entire reason we're having this discussion is based on people running auctions without stating the rules clearly up front (e.g. saying they are running the auctions "eBay style" when eBay has no multiunit identical item auctions).
Second, Auction House Beta ends up taking in $5 less. Running an auction house is hard work! If there are two generally reasonable sets of rules to choose from, I certainly won't begrudge the auction house choosing the one that nets them a little bit more in the end. I'm grateful there are auction houses available so I don't have to pay $250 for my PYPs.
You can always send the proprietors of Beta house a $5 tip if this is your concern.
Third, Auction House Beta offers less incentive for early bidding compared to Auction House Lambda. Early bidding helps auctions to succeed, and we all (bidders and auction house managers alike) want TD auctions to succeed.
Why do you say that? They both offer an identical incentive to early bidding, which is that you win the bid if two people bid the same amount and quantity can not satisfy both?
Also - consider this scenario:
3 identical items
A bids on 2 at $105
B bids on 2 at $100
C bids on 1 at $1
Lambda house results in: A wins two at $105, B wins 1 at $100 - right?
Beta house results in A wins two at $1, and B wins 1 at $1.
Beta House's outcomes are radically better for the bidders than Lamdba House's in this case (and never worse in any case).