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Grub with the partners of Sequoia Capital

grubwith.us

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Re: Grub with the partners of Sequoia Capital

#12
post #8

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…

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)

Re: Grub with the partners of Sequoia Capital

#13
post #8

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…

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.

Re: Grub with the partners of Sequoia Capital

#17

Starving entrepreneurs outbidding each other to sit with two rich guys? It is just me or does this seem backwards?

People seeking knowledge, experience, and advice outbidding each other to sit down with people with knowledge, experience, and advice. For charity. Doesn't seem so backwards to me.

Re: Grub with the partners of Sequoia Capital

#18
post #8

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…

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...

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