This comment was posted to the forum for my "Advanced game Theory" course
[I'm not sure how to deal with studying something that has immediate real world applications. It feels kind of dirty. (This may also explain why I got 36% on the most recent test /o\)]
I work for the New Zealand Treasury. It's a tradition here that every year, the incoming graduate recruits (typically a cohort of 10-15 bright sparks) must elect one member from amongst themselves to be chair of the Treasury social committee for the following year. The problem is that this responsibility is particularly bothersome, so a couple of years ago, when they couldn't agree on who should take the role, they decided to auction it off.
In particular, they ran a descending bid, second price auction. I.e. they started with a high initial price, and all bidders willing to accept the role at this price indicated their willingness. The auctioneer then gradually lowered the price so that one by one, individuals dropped out of the auction until only a single player remained; the 'winner' of the auction. The winner then took on the role of social committee chair for the following year, and all the other players split the costs evenly of paying the winner the last announced price (effectively the second lowest price amongst the bidders, as the winner would have announced something lower).
Superficially, this looks like the mirror image of an ascending bid, second price auction - which we know is efficient in the sense that it encourages truthfulness in dominant strategies. However, (to much outrage) I recently convinced my colleagues that this auction didn't have particularly nice properties, and that the outcome of their auction may not have been socially optimal. In particular, the auction encourages gaming, and there's no guarantee that the person with the lowest valuation will win the auction. Informally, my reasoning was as follows (this next section can be skipped if you can't be bothered):
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Consider my optimal strategy/best response function given the bids made by everyone else.
If my true valuation is lower than the minimum bid that was declared by the other players, then my best response would have been to undercut the minimum bid (it doesn't matter by how much because I receive the second price). This element of my best response function is fine, and is a desirable property in this setting.
However, if my true valuation is greater than the minimum bid that was declared by the other players, then my best response would have been to EITHER:
Just outbid the minimum bidder (even if this bid is lower than my true valuation). That way I minimise the payment that I (and all the other players) have to make to the winning bidder. Call this payment p.
Or, sometimes undercut the lowest bidder, even though this causes me to 'win' the auction and receive a negative payoff. This strategy is worthwhile when the amount that I save from avoiding the payment p exceeds the negative payoff I receive from winning the auction. Again, the amount by which I undercut doesn't matter as this doesn't affect the price I receive.
I reiterate, the reasoning above isn't formally accurate (e.g. it doesn't cover all possibilities properly, or ties...), but it's close enough to describing individuals' real best response functions in this setting. As a result, honesty is not, in general, a favourable strategy - especially if I think that it's unlikely that I'll win the auction. Moreover, there's no guarantee that that the person with the lowest cost of doing the job wins - as there are circumstances when it is desirable for an individual with a higher valuation to undercut.
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So - if you've stayed with me this my far - I would like help designing an auction for this year's graduate cohort (yes, I have been tentatively commissioned!). This auction should have the property of truthfulness in dominant strategies, and ideally, weak budget balance.
The best I've come up with so far is to require all n players to pay a fixed 'buy-in' price to participate in the auction - say $200. Then you could set the start price at $200n, and run a descending second price auction in which any remaining proceeds are donated to me. If my understanding is correct, this should be pretty much the exact mirror image of a second price sealed-bid auction and should therefore be strategy-proof (i.e. encourages truthfulness in dominant strategies). I think this should work because it removes the incentive for people to game their bids in order to minimise their payment p (as everyone pays the fixed cost of $200 regardless). However, this doesn't really solve the overall problem as you still need a mechanism to decide on what the buy-in price should be set at (ideally as low as possible as long as it's enough to cover the lowest true valuation).
One thing you should definitely be able to deduce from this post is that, for some reason, the New Zealand Treasury is not a renowned for its social life.
[Basically the problem is that it's easy to make people be honest about how much they value something if you don't mind making them pay money for it and keeping the proceeds at the end, but if you give the money back to the group afterwards it skews the results. The one reply so far suggests lying and saying he's going to keep the money then giving it back anyway, which the guy has pointed out is not a viable long term strategy]
This entry was originally posted at http://alias-sqbr.dreamwidth.org/504299.html. There are
comments.
I work for the New Zealand Treasury. It's a tradition here that every year, the incoming graduate recruits (typically a cohort of 10-15 bright sparks) must elect one member from amongst themselves to be chair of the Treasury social committee for the following year. The problem is that this responsibility is particularly bothersome, so a couple of years ago, when they couldn't agree on who should take the role, they decided to auction it off.
In particular, they ran a descending bid, second price auction. I.e. they started with a high initial price, and all bidders willing to accept the role at this price indicated their willingness. The auctioneer then gradually lowered the price so that one by one, individuals dropped out of the auction until only a single player remained; the 'winner' of the auction. The winner then took on the role of social committee chair for the following year, and all the other players split the costs evenly of paying the winner the last announced price (effectively the second lowest price amongst the bidders, as the winner would have announced something lower).
Superficially, this looks like the mirror image of an ascending bid, second price auction - which we know is efficient in the sense that it encourages truthfulness in dominant strategies. However, (to much outrage) I recently convinced my colleagues that this auction didn't have particularly nice properties, and that the outcome of their auction may not have been socially optimal. In particular, the auction encourages gaming, and there's no guarantee that the person with the lowest valuation will win the auction. Informally, my reasoning was as follows (this next section can be skipped if you can't be bothered):
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Consider my optimal strategy/best response function given the bids made by everyone else.
If my true valuation is lower than the minimum bid that was declared by the other players, then my best response would have been to undercut the minimum bid (it doesn't matter by how much because I receive the second price). This element of my best response function is fine, and is a desirable property in this setting.
However, if my true valuation is greater than the minimum bid that was declared by the other players, then my best response would have been to EITHER:
Just outbid the minimum bidder (even if this bid is lower than my true valuation). That way I minimise the payment that I (and all the other players) have to make to the winning bidder. Call this payment p.
Or, sometimes undercut the lowest bidder, even though this causes me to 'win' the auction and receive a negative payoff. This strategy is worthwhile when the amount that I save from avoiding the payment p exceeds the negative payoff I receive from winning the auction. Again, the amount by which I undercut doesn't matter as this doesn't affect the price I receive.
I reiterate, the reasoning above isn't formally accurate (e.g. it doesn't cover all possibilities properly, or ties...), but it's close enough to describing individuals' real best response functions in this setting. As a result, honesty is not, in general, a favourable strategy - especially if I think that it's unlikely that I'll win the auction. Moreover, there's no guarantee that that the person with the lowest cost of doing the job wins - as there are circumstances when it is desirable for an individual with a higher valuation to undercut.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
So - if you've stayed with me this my far - I would like help designing an auction for this year's graduate cohort (yes, I have been tentatively commissioned!). This auction should have the property of truthfulness in dominant strategies, and ideally, weak budget balance.
The best I've come up with so far is to require all n players to pay a fixed 'buy-in' price to participate in the auction - say $200. Then you could set the start price at $200n, and run a descending second price auction in which any remaining proceeds are donated to me. If my understanding is correct, this should be pretty much the exact mirror image of a second price sealed-bid auction and should therefore be strategy-proof (i.e. encourages truthfulness in dominant strategies). I think this should work because it removes the incentive for people to game their bids in order to minimise their payment p (as everyone pays the fixed cost of $200 regardless). However, this doesn't really solve the overall problem as you still need a mechanism to decide on what the buy-in price should be set at (ideally as low as possible as long as it's enough to cover the lowest true valuation).
One thing you should definitely be able to deduce from this post is that, for some reason, the New Zealand Treasury is not a renowned for its social life.
[Basically the problem is that it's easy to make people be honest about how much they value something if you don't mind making them pay money for it and keeping the proceeds at the end, but if you give the money back to the group afterwards it skews the results. The one reply so far suggests lying and saying he's going to keep the money then giving it back anyway, which the guy has pointed out is not a viable long term strategy]
This entry was originally posted at http://alias-sqbr.dreamwidth.org/504299.html. There are
comments.