We will purchase certificates in a descending price reverse auction, designed to ensure that:

- We spend exactly the intended budget.
- We maximize the total impact of purchased certificates.
- Participants cannot receive a higher offer by submitting a higher asking price: participants receive a single take-it-or-leave-it-offer for each project, based only on the other participants’ asking prices and our evaluation of each project’s impact. We assume that applicants will accept this offer if and only if it is higher than their asking price.

These criteria essentially uniquely determine the auction design.

In order to preserve incentives, we will make a reasonable effort to avoid knowing the asking prices before completing our impact evaluations.

## The basic auction

We start with a very high (infinite) offer price per unit impact, and imagine gradually lowering that price. At each price, we ask “How much money would we spend if we purchased all certificates which are available at this price?”

As we lower the price the expected expenditure will fall: it starts at infinity, and reaches 0 once the offer price is below the cheapest asking price.

As soon as the expected expenditure is equal to our budget, we purchase all certificates available at the current price.

## Details

The basic auction is not quite satisfactory:

- The expenditures may fall discontinuously, and so may never meet exactly the intended budget.
- Each participant implicitly competes with themselves, compromising incentives.

To fix these issues, for each price *and for each participant*, we estimate how much money we would spend if we excluded that participant from the auction and then purchased all other certificates available at that price.

As we lower the price, some of these expected expenditures will fall below our available budget. If we are considering price *p*, and we find that excluding a participant Alice would leave us unable to spend our remaining budget, then we buy some certificates from Alice at the price *p*. We buy exactly enough certificates from Alice that we could spend the rest of our budget at price *p* without buying any more certificates from Alice.

We do the same for each user. Once we could spend our entire budget at price *p*, even excluding any single user, we lower the price and continue the process.

*Note**: if there is a single applicant, this procedure would give them the entire budget in exchange for nothing. This is the intended behavior and we would implement it. However, if there are particularly few applicants during a round, we may encourage additional participation and/or delay the end of the round.*

## Sequential auctions

We will conduct a separate auction in each round, buying $1,000 of certificates each time.

It may happen that the price of certificates varies from one round to the next. If there are very few applications in the first round, we will need to pay a very high price, which may fall in future rounds. Conversely, if we only receive offers in the first round, then the price will rise as we purchase the cheapest certificates in early rounds.

If prices rise from one round to the next, we will increase the payments to participants in earlier rounds accordingly. If prices fall from one round to the next, the earlier payments will stand. This ensures that there is no strategic advantage from delaying a submission, or from posting a higher asking price in order to be selected in a later round.

(The implementation of this “topping up” is essentially the same as the original auction. Whenever we purchase any certificate at a price *p*, if we have previously purchased another certificate at a price *q* < *p*, we will first top up the previous purchase by paying an additional (*p* – *q*). When considering how much we would spend at a given price, we will include all payments to previous rounds’ participants that would occur if we were to make a purchase at that price.)