[orijing]

It's a great idea. However, unless I'm mistaken, I believe his auction mechanism is not any of the standard "revenue maximizing" OR "social utility maximizing" mechanisms. The "maximum amount you would pay for this meal" suggests the meal's value to you.

However, for all K=# of seats, his Kth-price auction does not have the property that inputting your truthful value is your dominant strategy. The price should really be the bid of the K+1th person--otherwise, the Kth person can lower his bid in any outcome to the K+1th price/value (in descending order) and still obtain the seat. So it is not even a Nash Equilibrium to submit your truthful value.

So let's see how we can make the auction consistent with the desire to get everyone to bid their truthful value. If instead, the auction price was based on the 9th highest bid (which we assume to be the value) OR the reserve price (whichever one is higher), then it is everyone's dominant strategy to bid their value.

I don't want to rehash examples taught in an introductory Auction Theory class (which I greatly enjoyed), so if you're interested, take a look at http://en.wikipedia.org/wiki/Vickrey_auction

It's basically a fancy name for what I described, plus a few modifications and extensions.

[greattypo]

More simply, in a second-price auction, there is 1 winner, and you clear at the 2nd highest bid.

With 8 winners, they should be clearing at the 9th highest bid.

Of course you don't have to do it this way, but it's the least game-able outcome.

It's clear they had the second-price/Vickrey style in mind, and they came awfully close to getting it right.

[klochner]

It's actually the multi-unit analogue of the first-price sealed bid auction.

Note that in FPSB you also don't have an incentive to report your true value, but it is revenue maximizing and efficient in expectation assuming risk-neutral bidders [1].

The basic gist of the proof is that everyone has an incentive to shade their bids down in proportion to the probability that their bid sets the price. The amount you shade is monotone in your valuation, so you end up with the same relative ordering of bids.

And the punchline is that you get the same winner and the same expected revenue for the Vickrey vs. FPSB.

[1] http://en.wikipedia.org/wiki/Revenue_equivalence_theorem#Rev...

[orijing]

Yeah, it might be what they were after, but their text (How much are you willing to pay?) suggests that your dominant strategy is to input your true value.

If that's what they're after, the text is misleading in my opinion...

[leif]

They taught this principle to all new google hires and interns as part of orientation when I interned there, whether you were working on ads or not. It was a nice "this is how the company you work for pays you" type thing, I liked it.

(and you are not mistaken, unless I am mistaken)