Perhaps this is a more theoretical answer than what you’re looking for, but this kind of thing can be a problem in combinatorial auctions, even though they’re designed to find a globally optimal allocation of goods.
Just think of the road segments as individual goods, with bidders (drivers) making bids on bundles of roads they intend to use. The auction then finds the best possible allocation of roads (maximizing the sum of bidders’ reported utilities), and charges the winners some amount of money via a pricing rule (see below).
A pricing rules often used in auction is VCG (Vickrey-Clarke-Groves). Instead of paying your bid on the bundle that you won, you just have to pay the externality you impose on others by participating in the auction, which is always less than your winning bid. This is super nice because it makes the auction strategyproof, i.e., it’s a dominant strategy to reveal your true values for each bundle of road segments.
Now, you would expect that when more goods are introduced, the competition for those goods must decrease, making prices cheaper on average. However, under VCG payments you don’t have this kind of monotonicity: adding a road segment to the supply can increase the VCG payments while leaving the allocation unchanged. That’s a recreation of the paradox, just in a different domain.
I’m just sticking with roads as the example, but this might in principle happen in any auction where goods are complements (= bidders might value a bundle more than the sum of the individual goods it’s made of).
Thanks. I was hoping to get real-world examples, but yeah this is interesting and does seem structurally similar. Though, an auction sort of seems like it’s structurally assuming “total inelasticity”, like there’s just a fixed pile of goods that you’re auctioning off (and then external to that we can compare two auctions with different goods), contrasting to markets, which I imagine are mostly at least somewhat supply-elastic (though maybe that’s a wrong imagination, and certainly on shorter time-scales there’s lots of supply inelasticity). I can’t immediately think of examples where anyone is bidding, in a fixed-supply auction setting, on goods over which they have multiple overlapping non-linearly-combining utilities. Like, are the ever companies literally bidding on contracts, where they have non-linear utilities over combinations, with a Braess-like combinatorial pattern? I don’t see why that would happen in practice; it makes sense to want either (B and B’) or (C and C’), because, say, the capability to fulfill contract B overlaps with the capability to fulfill B’..… oh okay maybe this would happen if then someone invents something that makes fulfilling C and B’ much more overlapping than before? Does that ever actually happen?
Perhaps this is a more theoretical answer than what you’re looking for, but this kind of thing can be a problem in combinatorial auctions, even though they’re designed to find a globally optimal allocation of goods.
Just think of the road segments as individual goods, with bidders (drivers) making bids on bundles of roads they intend to use. The auction then finds the best possible allocation of roads (maximizing the sum of bidders’ reported utilities), and charges the winners some amount of money via a pricing rule (see below).
A pricing rules often used in auction is VCG (Vickrey-Clarke-Groves). Instead of paying your bid on the bundle that you won, you just have to pay the externality you impose on others by participating in the auction, which is always less than your winning bid. This is super nice because it makes the auction strategyproof, i.e., it’s a dominant strategy to reveal your true values for each bundle of road segments.
Now, you would expect that when more goods are introduced, the competition for those goods must decrease, making prices cheaper on average. However, under VCG payments you don’t have this kind of monotonicity: adding a road segment to the supply can increase the VCG payments while leaving the allocation unchanged. That’s a recreation of the paradox, just in a different domain.
I’m just sticking with roads as the example, but this might in principle happen in any auction where goods are complements (= bidders might value a bundle more than the sum of the individual goods it’s made of).
Thanks. I was hoping to get real-world examples, but yeah this is interesting and does seem structurally similar. Though, an auction sort of seems like it’s structurally assuming “total inelasticity”, like there’s just a fixed pile of goods that you’re auctioning off (and then external to that we can compare two auctions with different goods), contrasting to markets, which I imagine are mostly at least somewhat supply-elastic (though maybe that’s a wrong imagination, and certainly on shorter time-scales there’s lots of supply inelasticity). I can’t immediately think of examples where anyone is bidding, in a fixed-supply auction setting, on goods over which they have multiple overlapping non-linearly-combining utilities. Like, are the ever companies literally bidding on contracts, where they have non-linear utilities over combinations, with a Braess-like combinatorial pattern? I don’t see why that would happen in practice; it makes sense to want either (B and B’) or (C and C’), because, say, the capability to fulfill contract B overlaps with the capability to fulfill B’..… oh okay maybe this would happen if then someone invents something that makes fulfilling C and B’ much more overlapping than before? Does that ever actually happen?