You’re right that it’s similar to a Vickrey auction in that the 2nd highest bid (in the 2-player case) is used as the price
It’s very much a first-price auction; here, you’re minimizing loss instead of maximizing gain. If you add a third person who bids $10 to pick up the kids, that person does it (because they’re the lowest-cost option).
The good is jointly owned
Actually, wouldn’t it make sense to only pay the winner 1/n of their bid (from each other participant)? In the case of picking up the kids, the union has received a negative windfall, and is attempting to price it. The cheapest solution is $15, so the cost is $15- which is then borne entirely by one party!
Now, this is assuming that people are pricing their bids at indifference ($15 completely compensates for having to pick up the kids), which may not be the case. You could try to equate B’s regret at paying D’s price and D’s dissatisfaction with having to perform the task, but this seems silly compared to pricing indifference.
Alternatively, rather than trying to allocate the windfall equitably (which leaves both parties worse off by the same amount, but with different levels of surplus), you could try to equalize surplus- which would be B paying D $42.50. I think this makes the incentives inside the bidding stronger, but makes the incentives on when to bid more troublesome, because this encourages you to yootle when the other person has a lot at stake.
I’m impressed! That’s kind of the conclusion we gradually came to as well, after a lot of trial and error. Better to not have people feel like their desperation is being capitalized on.
Another way to put it: when you’re really desperate to win a particular auction it’s really nice to be able to just say so honestly, with a crazy high bid. Trying to allocate the surplus equitably means that I have to carefully strategize on understating my desperation. (And worst of all, a mistake means a highly inefficient outcome!)
PS: To be clear about first-price vs second-price, it’s technically neither since there’s no distinct seller.
Here’s the n-player, arbitrary shares version:
Each participant starts with some share of the decision.
Everyone submits a sealed bid, the second-highest of which is taken to be the Fair Market Price (FMP).
The high bidder wins, and buys out everyone else’s shares, ie, pays them the appropriate fraction of the FMP.
“Even yootling”, or just “yootling”, refers to the special case of two players and 50⁄50 shares.
In that case, instead of bidding a fair market price (FMP), you say how much you’re willing to pay if you win.
True FMP is twice that, since you only have to pay half of FMP with even yootling.
So instead of deciding what you’d pay, doubling it to get FMP, then halving FMP to get the actual payment, we short circuit that and you just say the payment as your bid.
For yootling with uneven shares it’s easier to bid FMP and then pay the appropriate fraction of that.
It’s very much a first-price auction; here, you’re minimizing loss instead of maximizing gain. If you add a third person who bids $10 to pick up the kids, that person does it (because they’re the lowest-cost option).
Actually, wouldn’t it make sense to only pay the winner 1/n of their bid (from each other participant)? In the case of picking up the kids, the union has received a negative windfall, and is attempting to price it. The cheapest solution is $15, so the cost is $15- which is then borne entirely by one party!
Now, this is assuming that people are pricing their bids at indifference ($15 completely compensates for having to pick up the kids), which may not be the case. You could try to equate B’s regret at paying D’s price and D’s dissatisfaction with having to perform the task, but this seems silly compared to pricing indifference.
Alternatively, rather than trying to allocate the windfall equitably (which leaves both parties worse off by the same amount, but with different levels of surplus), you could try to equalize surplus- which would be B paying D $42.50. I think this makes the incentives inside the bidding stronger, but makes the incentives on when to bid more troublesome, because this encourages you to yootle when the other person has a lot at stake.
I’m impressed! That’s kind of the conclusion we gradually came to as well, after a lot of trial and error. Better to not have people feel like their desperation is being capitalized on.
Another way to put it: when you’re really desperate to win a particular auction it’s really nice to be able to just say so honestly, with a crazy high bid. Trying to allocate the surplus equitably means that I have to carefully strategize on understating my desperation. (And worst of all, a mistake means a highly inefficient outcome!)
PS: To be clear about first-price vs second-price, it’s technically neither since there’s no distinct seller.
Here’s the n-player, arbitrary shares version:
Each participant starts with some share of the decision. Everyone submits a sealed bid, the second-highest of which is taken to be the Fair Market Price (FMP). The high bidder wins, and buys out everyone else’s shares, ie, pays them the appropriate fraction of the FMP.
“Even yootling”, or just “yootling”, refers to the special case of two players and 50⁄50 shares. In that case, instead of bidding a fair market price (FMP), you say how much you’re willing to pay if you win. True FMP is twice that, since you only have to pay half of FMP with even yootling. So instead of deciding what you’d pay, doubling it to get FMP, then halving FMP to get the actual payment, we short circuit that and you just say the payment as your bid. For yootling with uneven shares it’s easier to bid FMP and then pay the appropriate fraction of that.