Permit bidding games: What this year's Nobel Prize in economics has to do with climate action

Today is the 124th anniversary of Alfred Nobel's death, time for this year's coveted medals. The Sveriges Riksbank Prize in Economic Sciences goes to Paul R. Milgrom and Robert B. Wilson, both from Stanford University, "for improvements to auction theory and inventions of new auction formats". Stuff for geeks and Sotheby's? Sure, but you should be interested, too. Their work is already affecting you.

There are the standard examples. If you're active at online marketplaces like eBay or Taobao, you know Paul's and Robert's work in action. Wondered where the price of your mobile contract comes from? Here we go. Find tons of other examples in Paul's excellent text Putting Auction Theory to Work.

But Paul's and Robert's work also has left a footprint in a domain that you might not come up with when confronted with the term "auction". Your environment.

Price-tagging carbon emissions

To combat climate change, we must decarbonize the economy. It's consensus that attaching a price tag on greenhouse gas emissions is the best method for the objective. One way to do this is a cap-and-trade scheme, like the EU Emissions Trading System (EU ETS). The government issues permits (in the EU ETS they are called "allowances", or EUAs) that allow the owner the emission of one ton of carbon dioxide each. The number of permits is limited in such a way that it is (ideally) consistent with mitigation targets. Emitters will be willing to pay a sum of money for a permit up to the cost of abating a ton by technical means. Simple economics.

The cool thing is that a cap-and-trade scheme works even if the government gives away the permits for free. Then trade between emitters at an exchange will make a market price, just like it does for bonds or stocks at Wall Street. But this "grandfathering" of permits is a bit at odds with what most people consider fair, namely that those that mess up should clean up, or pay for it

Here is where auctions come in.

Permit bidding games

In principle, the government could just set a price, or differentiated prices, and offer the permits TIOLI (take it, or leave it). However, what is a reasonable price? There would be endless debate about this issue. I mean, having not to set a price but a quantity is the whole point of a cap-and-trade scheme in in the first place.

Let just competition do the job! Like in a Sotheby's auction of a vintage Ferrari, competitive bidding will drive the price of a permit for sale up until there is a winner. Sold. We have a price. Plus, a goodie for the treasury.

But Paul, Robert, and many others (by the way, the work for which Leonid Hurwicz, Eric S. Maskin, and Roger B. Myerson got the 2007 prize is intimately related) showed that the details matter. Should the winner pay a price equal to her winning bid like in a classical English auction? Or should the price be set equal to the next highest bid, like on eBay? And before there is winner, should the price be driven up during bidding, or down like in a Dutch auction? Should the bids be publicly observable at all, or placed secretly in sealed envelopes? If so, a single shot, or are multiple bids allowed? Should there be a minimum price? Should all permits be auctioned off in single round, or in multiple packages? On a single date, or during an extended period?

Tons of questions like these arise when setting up a real auction from scratch. Paul, Robert and others demonstrated that microeconomic theory and game theory help a lot in thinking straight about them. More recently, behavioral experiments proved merit as well. In a nutshell, seemingly minuscule changes in the auction rules can result in significant changes in bidder behavior, which in turn determines the allocation of the exchanged objects and the prices paid.

But enough theory. Let's get down to the floor.

An almost real permit auction

The EU's commitment to the polluter-pays principle is the basis of the provision in the EU ETS rules that, eventually, all EUAs should be auctioned off. For a number of political reasons, several sectors and member states are partially exempt from this default, such that currently a bit below half of the EUAs are still "grandfathered". This fraction is supposed to go down to almost zero by 2030. Let's see.

Anyway, let's participate hypothetically in one of the auctions to see how it works. It's Thursday, 9am CET, welcome to the European Energy Exchange (EEX) in Leipzig, Germany. We went through the auction rules set out in the EU ETS Auctioning Regulation and the amendment for the 2021-2030 trading phase, and we are ready to get our lot of 500 EUAs that we need for our cute little blast furnace. 

Including the trading and clearing fee (€1,68), we can afford to pay 20 grand for the lot, otherwise it's cheaper to shut down the furnace for the month. About 20 other bidders are in the room, some really large corporations going for thousand lots or more. 7,903 lots are for sale today, that's permits for slightly above 3.9 million tons of carbon emissions.

Ring ring, the two-hour bidding window is open. We're in a single-round, sealed bid, uniform, clearing-price auction. What the heck does this mean? Let's proceed.

Within the next two hours, we can place any number of bids. Each bid specifies the number of allowances the we like to buy at a given price. Okay, the first part is easy, we want a full lot, that's 500 EUAs. But what price should we bid? I mean, €40 per allowance is our upper limit, but a smaller price is a good thing. But if our bid is too low, we might come away empty-handed.

Here is auction design in action. How exactly is our bid related to the chances of being successful and the price we are going to pay? 

Rules matter

There is a myriad of different approaches to make the connection between bids, allocation, and price. Again, have a look in Paul's book. The crux is that those rules have consequences. In our permit auction, they will have an impact on the price paid for a permit to emit a ton of greenhouse gases. Just the rules, independently from the fundamentals. Auction by auction, year by year, those rules will leave a footprint in the dynamics of climate change. I think that's enough reason to think about auction theory already.

Back in Leipzig. Our auction is sealed bid, that is, we will hand in a (virtual) envelope that is unobservable to the other bidders until the end of the auction. Likewise, we don't know the bids of the other participants. This is an especially important feature because it significantly reduces the scope for strategic bidding behavior. We cannot respond directly to other bids, and the other participants cannot respond to our bid. Game theorists call such a situation simultaneous game, not in a literal but in a strategic sense, because effectively all bidders reveal their bid simultaneously at the time the envelopes are opened. This is quite different to the classic English auction or the Dutch auction, in which bidders place bids sequentially. They are plagued with dynamic strategies such as "bid sniping" and there is a risk of crazy overbidding, or as Max Bazerman and Will Samuelson put it: "I won the auction but don't want the prize". Our sealed bid is straight: think, write down, submit, wait. 

But we are still stuck at the first stage. What price to bid? In an English auction there is a nasty trade-off, because if we win, we pay a price equal to our bid. A high bid increases the chances of winning, but also the price we have to pay. A low bid lowers the price, but also the chances of being successful.

The uniform clearing price rule we have here in Leipzig is a clever trick to vaporize this trade-off. All successful bidders pay the same price, regardless of the price they specified in their bids. This makes the price we have to pay independent from our bid, just like in eBay's second-price auction format, in which the successful bidder pays a price equal to the next-highest bid. With such independence, we can safely bid our limit price of €40 per EUA, because that maximizes our chances of being successful without affecting the price we are going to pay if so (except in the unlikely case in which our bid is pivotal). Envelope dropped.

Ring, ring, it's 11am, the bidding window is closed. Now, like a bookmaker, the EEX reads the bids, makes a list, and determines at which price the demand for allowances equals the number of allowances offered for sale in the auction. This is the clearing price. Today, 3,951,500 EUAs were for sale, bids for 5,872,500 were submitted, the clearing price is €30.04. Yay, we're among the 21 successful bidders. Find those results of the real auction held today on December 10th, 2020, here or here.

From prizes to prices

Is €30.04 a reasonable price for a ton of carbon emissions? From a social perspective, it's not way off. But ask yourself: with an average passenger car currently on the market you can drive about 8,000 km with a ton of carbon emissions. Most people cover around 12,000 km per year. What would be your bid, if the alternative is leaving the car in the garage?

The headline image is based on a photograph by Nicholas Cappello under non-commercial license.

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