Well, not quite the first. Bethany and Danny auctioned off commitment contracts informally by email in 2010. But this is the first one that was somewhat formalized, later in 2010.
The interface worked like so: You add your name and your bid. Everyone else can see you doing so in real time. Click recalculate any time to see how the bids translate into shares of the commitment contract everyone owns. Owning some fraction of the commitment contract means that you get paid that fraction of total amount forfeit by the person who made the commitment.
The total amount paid for the commitment contract also implies market odds that the person will actually pull off what they committed to.
At any time you can decide to increase your bid by just putting a higher number after your previous bid. Lower bids aren’t allowed. Each bid you place is a commitment of your own. But you’ll generally pay less than your final bid. Read on for how that works.
It’s a proxied, ascending Chinese auction for a divisible good!
Short version: Decide the most you’d possibly pay for the chance at the full $600 if Melanie fails. Bid that. That’s the optimal strategy.
Longer version:
Anyone can enter a bid at any time and you can revise your bid upward
at any time. You can’t lower your own bid but you don’t have to beat
anyone else’s bid. Every time a bid is made the mechanism computes
what share everyone is currently getting and what they’ll have to pay
for it. As long as that sounds like a bargain, keep upping your bid to
increase your share!
Again, you should think of your bid as the most you’d pay for the whole contract.
Your payment will be computed as some fraction of that for some fraction of the $600 jackpot.
A fraction of the $600 Melanie will be forfeiting if her weight crosses the bright red line at bmndr.co/mo/weight. That red line takes her to 160 pounds “eventually”: She cannot gain weight (bright red line is flat) and whenever she loses weight (goes below the line), it ratchets down to lock in her progress. As long as she’s below the red line she can stay flat indefinitely. But like all Beeminder contracts, a single day above the line and she forfeits the money. Full contract at doc.bmndr.co/mominder.
You don’t need to know that to play but since (we’re pretending) you asked:
Given the vector of bids, b, let
n = |b| and let
r = sum_i 1/b_i.
Then i’s payment, p_i = (n-1)(r-(n-1)/b_i)/r^2.
But if the p_i corresponding to the smallest b_i is negative then set p_i = 0 and repeat recursively with the remaining bidders.
The bids are taken to be everyone’s common knowledge valuations and then the payments are computed as the Nash equilibrium bids in a Chinese auction.
I thought it would be strategically tricky because you could place a bid to get a nice chunk of the contract and then someone comes along and bids way more. So now you’re paying your bid but getting only a sliver of the contract, which would suck. We could allow people to reduce their bids if that happened but I thought that could make the bidding fail to ever end. People might keep shifting their bids up and down in response to each other forever and never be happy. So this mechanism tries to have the best of both worlds. The bidding will end because you can only increase your bid — at some point you’ll max out. And the other problem is solved because what you pay automatically goes down if higher bidders come along after you. Another advantage of this mechanism is that you can decide the true maximum that you’d pay for the entire contract and just enter that as your bid and you’ll (theoretically, but maybe also really) get the best possible deal that way automatically.
An English outcry auction? Well, we wanted to spread out the ownership of the contract.
In a Chinese auction there are an unlimited number of tickets available for a penny apiece. At the end, whatever fraction of the tickets you own, that’s what fraction of the good you win.