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On eBay, bidding the highest you're willing to pay is not always optimal, because bids are not sealed, and other bidders may not be putting in their highest value, and there's a specific time it ends. Only the highest bid at any time is sealed.

If your opponent would bid, say, $500, but it's currently at $400, they might only put in a bid for $425, and if you bid more than that right before it ends you can get it for $430. While if you'd bid $475, then your opponent might have bid it up to $480, causing you to end up paying more.

Is anyone actually irrational in this scenario? I suppose anyone not using sniping tools and also not bidding their highest price is, or at least they could get a strict improvement by doing so. Given that other players aren't rational, the whole assumptions break down.

The rational bidding strategy on EBay is to always place 1 bid at the maximum price you're willing to pay. The problem is that humans aren't rational. Some people place winning the auction higher on their priority list than bidding within their budget.
There is also an element of uncertainty. Sometimes you are ready to pay more but you are unsure of the value. Others bidding more, may convince you it is ok to bid more.

For example, foreign jewellery on which you are unfamiliar with the hallmarks. You don't mind paying $200 for it if it is silver, but is it ?

Of course, rationally, for the raison you gave, you should not use that, but conversely if you are familiar with a certain type of popular auction you start to see some patterns. An object that breaks it is either a bargain, a fraud or you were simply early.

For example, silver never goes for less than scrap and genuine auction never really shoot way over boot sale value.

Or maybe I rationalised my irrationality :-)

I wish Ebay would extend the auction for ten minutes every time there is a new bid, the current situation isn't good for sellers.
If they do that they should also allow the seller to accept bids and end the auction.
No. Consider many similar items being sold at one time by one seller (common scenario). By bidding what you think "it's worth" up front, you announce to the competing bidders what you are willing to pay. You are much better off waiting until the last minute then bidding slightly higher than the current bid on every item.
You are not really announcing it, due to the second price nature of the eBay "bidding agent", but tough luck when two high price bidders happen to bid on the same copy. With multiple auctions, bidding becomes surprisingly tactical.
It's trivial for them to see that you've auto-bid because of the increment and the speed at which a second bid is placed if they place one higher. So you are kind of announcing it. And on similar items, they can work one up to your limit, determine the limit, then return to best it on all the other items at the last minute.
I gave a scenario where that doesn't work. It's only rational if everyone else does it. If some people won't do it, then by raising the price early you may induce them to bid higher, which is bad for you.
Unless you enjoy misery, trolling, and derive satisfaction from forcing other people to make stupid decisions.

Personally I'm more than happy losing a bid if I make someone else suffer winner's curse just because they are blinded by escalation of commitment and a long list of other biases.

One of my favourite speeches touching on the subject: The Psychology of Human Misjudgement - Charlie Munger Full Speech

bit about auctions is at 59:30 https://youtu.be/pqzcCfUglws?t=59m30s text https://buffettmungerwisdom.files.wordpress.com/2013/01/mung...

It's not bad if they bid higher than you - you being a rational person would know that you'd be unwilling to pay higher than your only placed bid, so you aren't really "losing" anything
It's bad if, if you wouldn't have bid so high, you'd have been able to win at the end with a lower bid than your highest.
Ebay bidding theory is a convoluted mess once you start considering multiple concurrent auctions for similar items that may or may not be perfect substitutes for different bidders.
Even with only two bidders and only one item, the scenario I described can take place, showing that assuming other bidders are rational and well informed about sniping tools is required for the theorem to obtain.
If everyone is rational (ie., won't purposely screw themselves.) and does not change their maximum amount according to what other bidders do, then it kind of doesn't matter in the end.

[1] https://en.wikipedia.org/wiki/Revenue_equivalence

A Vickrey auction is much more interesting (and complex) when there are dozens of bidders, each with their own budget, and multiple products. Then the solution turns into a profit maximization algorithm, with the highest bidder not necessarily winning each item.
So Böttiger ratted Goethe out. It's unfortunate that Goethe figured out the Vickrey auction, but not the principal-agent problem.
I see how his agent sharing the contents of the envelope hurt Goethe's attempt to gather intel for future auctions, but the outcome of the sealed envelope auction was unchanged, or am I misunderstanding? Goethe had 1000 talers as his minimum price so no matter what Vieweg offered, so long as it was above 1000 Goethe was never going to make more than that.

For this reason I find the last paragraph of the article confusing:

> Hermann and Dorothea went on to be a bestseller, earning tens of thousands of talers for Vieweg and nary a penny more for poor Goethe.

The article clearly states that the purpose (in theory at least) was not merely to get 1000 talers but to also get a better estimate of the publisher's perceived valuation of Goethe's work.
A pity that you propose the problem but not a solution. What would you propose to overcome the principal-agent problem in that regard? A tournament between different lawyers (proposed solution by wikipedia for prinipal-agent problem) doesn't really seem to work since it would only make sense after comparing the results of many transactions and of many lawyers.
Great example of how auctions can bring benefits to both parties (as long as you can trust the middle man)
So he used a single bid auction with a hidden reserve, and the sale price won't exceed the reserve, so the seller either gets the exact price they demanded or no sale at all.
All that and they don't tell us how much Vieweg actually bid?
It's right in the end: Goethe's lawyer revealed his reservation price of 1000 talers to Vieweg and he bid just that.
It doesn't say "he bid just that" explicitly.
Oops, I guess you're right about that. I took the expression "nary a penny more" to mean "nary a penny more [than 1000 talers]", since I assumed that Vieweg still bought the manuscript. I see now that this isn't explicit at all.

But Moldovanu & Tietzel (1998) [0] do report in their article that "Vieweg offered exactly that sum [1000 thalers]". So there it is!

[0]: https://www.econ2.uni-bonn.de/pdf/papers/goethes_second.pdf

Good find!