Many thanks to Thomas Thiery and Barnabé Monnot for discussions on this topic.

Ethereum relies on a decentralized validator set to build blocks that uphold chain neutrality. The idea is that transactions one party may censor are not censored by all parties in the decentralized validator set. MEV-Boost uprooted this way of including censored transactions as block building is now primarily done by a small set of sophisticated builders whose preferences for including transactions are not necessarily aligned with the validator’s preferences or network stakeholders broadly.

The min-bid parameter in MEV-Boost functions as a secret reserve price that allows the validator to attach some valuation to its preferences. For example, if a validator has a valuation of 0.05 ETH for building a block themselves, they can set the min-bid parameter in MEV-Boost to this value. The validator then self-builds if the highest bid obtained via the MEV-Boost auction is less than this value and outsources block construction otherwise.

If we assume validators do not censor transactions, then allowing validators to express their preferences in this way decreases the delay for censored transactions to be included while allowing validators to benefit from MEV revenue when this revenue is high. This was the original reason why the min-bid parameter was proposed.

The min-bid parameter elegantly balances weak censorship resistance with strong censorship resistance. Weak censorship means all transactions that pay the necessary fees will eventually be included, although certain censored transactions may experience some delay. Strong censorship means censored transactions will never be included. Strong censorship could happen when a minority of validators who do include censored transactions are re-orged out of the chain by the majority of validators. Allowing all validators, regardless of sophistication, to benefit from high MEV opportunities ensures that the validator set will stay decentralized and, therefore, prevents strong censorship. Allowing validators to self-build when MEV opportunities are low increases the network's weak censorship resistance, as censored transactions are included faster.

In practice, the min-bid parameter seems to work quite well. Data analysis by Data Always found a lower bound of 6.5% of proposers using the min-bid parameter. Building on this, 2.65% of all blocks revert to local block building because of min-bid, contributing to about 7% of non-censored blocks in total.

This post explores whether we can make small improvements to the min-bid parameter. The root of its inefficiency is that it is secret. A validator first runs the MEV-Boost auction, and ex-post sees whether the highest bid exceeds the min-bid value. This means that the reserve price does not influence the bids in the MEV-Boost auction.

Let us introduce a little bit of notation and analyze the potential outcomes of the MEV-Boost auction. Let v_max denote the highest valuation for the block amongst all bidders. Let b_max be the bid of the bidder with the highest valuation and assume that bids are non-decreasing in valuation. Let r_min be the reserve price of the validator. We could then end up in three situations

1. v_max > b_max > r_min. The highest valuation and bid are higher than the secret reserve price, and the proposer sells its block-building rights to the highest-paying builder.

2. r_min > v_max > b_max. The highest valuation and bid are lower than the secret reserve price, and no transfer occurs.

3. v_max > r_min > b_max. The highest valuation is larger than the secret reserve price, but the highest-paying bid is lower than the secret reserve price. No transfer occurs.

The secret reserve price is irrelevant in the first case. The second case demonstrates the reserve price's intended use. The third case, however, is problematic. Block-building rights are not allocated to the agent that values it the most, the builder with the highest valuation, but instead to the proposer.

If the reserve price were public, the third case would not occur because the builder with the highest valuation would bid at least the reserve price. If the reserve price is set to how much the proposer values self-building, publicly revealing the reserve price means that the block-building rights should always be allocated to the agent that values them the most. The property of allocating the block-building rights to the agent that values it the most is called allocative efficiency and could be a desideratum of allocation rules.

Now assuming a public reserve price, the expected welfare gain is Pr[Third case] * (v_max - r_min). The problem is that the builder solely realizes this welfare gain since the builder only needs to pay the proposer exactly the value that the proposer assigns to keep the block-building rights. Can the proposer do better and capture part of this welfare gain?

Let v_keep be the value that the proposer assigns to keeping the block-building rights. Up until now, we have assumed that r_min = v_keep, but strategic proposers could set a reserve price that is higher than their actual value r_min > v_keep. Setting a higher reserve price excludes more builders (increases the probability of ending up in the second case) but increases the revenues when the builder with the highest valuation would bid under the reserve price if it were secret (akin to the third case).

It turns out that setting a reserve price that is higher than the value that the seller attaches to the item, r_min > v_keep, can increase revenues under certain conditions. This idea is called the exclusion principle in auction theory. The intuition is that a seller excludes buyers with very low valuations, those whose valuations are lower than the reserve price, but the seller increases revenues when there is a single buyer with a higher valuation. The probability of the former happening is low as all bidders need to have lower valuations than the already low reserve price. The probability of the latter happening is slightly higher because all but one of the bidders must have valuations that are lower than the reserve price, but the valuation of the highest bidder must be higher than the reserve price.

I purposefully avoid attaching any specific model to this because the MEV-Boost auction is a complicated auction that somewhat resembles an English auction. However, it is also time-constrained, has no perfectly competitive market, and the interdependencies between builder valuations vary over time. This post aims to raise the idea that the exclusion principle can be used in MEV-Boost, not to propose an optimal way of setting reserve prices.

One could argue that publicizing the min-bid parameter decreases the network's weak censorship resistance. While it is likely that fewer blocks revert to local block-building because of a public reserve price, this only happens in very few blocks anyway. Moreover, I believe we should not celebrate the third case presented above because neither the proposer nor the builder is happy with the outcome.

If strategically setting reserve prices increases expected revenues, then more proposers will use the min-bid parameter. Although the expected revenues are higher, a higher reserve price will also lead to more locally built blocks; hence, in equilibrium, the number of locally built blocks may actually increase while we rely on altruism less.

Implementing public reserve prices could be very straightforward. The simplest way would be for proposers to message builders or relays with their reserve price. Relays could choose to enforce the reserve price or not. If relays do not do so, builders may doubt the credibility of the reserve price, decreasing their bids. A proposer may still accept a builder bid below the public reserve price they broadcast if they wish to do so according to a private min-bid value. If relays do enforce the reserve price, credibility is not so much a problem.

Finally, relays could implement entry fees, a fixed and nonrefundable amount that bidders must pay to the auctioneer to be allowed to place a bid. Auction-theoretically, this is similar to setting a reserve price. Bidders with very low valuations are excluded, while those with higher valuations pay slightly more. Relays could help users strategically set entry fees or reserve prices and share the profit. This could be a way to monetize relays.

As an example, proposers could privately communicate their true value for locally building a block to the relay. This value could be zero. Then, the relay suggests a strategic reserve price that the proposer could publicly broadcast through the relay. If the highest bid is indeed the reserve price, the proposer and relay could share the difference between the strategic reserve price and the true reserve price of the proposer. Similarly, the relay could strategically set an entry fee based on the proposer's true value for building the block locally, and the proceeds of the entry fee could be split between the proposer and the relay.

What the equilibrium effect of publicly broadcasting min-bid on censorship resistance is is difficult to ascertain. This post does highlight a potential way for sophisticated proposers to extract more MEV than less sophisticated proposers which is bad for strong censorship resistance. Relays could take the burden of this sophistication, potentially increasing the viability of neutral relays, but also increasing their importance in the ecosystem. Finally, fewer blocks will revert to local block building for proposers currently using the min-bid parameter and who will set a public, not but strategic, min-bid. However, potentially, more blocks will revert to local block building for proposers that will set a public reserve price in order to gain more revenues but currently do not use the private min-bid parameter.

If you want to implement public reserve prices into mev-boost or a relay, please get in touch with me!

P.S.: In this note, we have assumed that secret reserve prices are not considered in builders’ bidding strategies. Since only 6.5% of proposers reportedly use the secret reserve price, I believe this is a fair assumption. Moreover, if it is a proposer’s goal to increase revenues by influencing builders’ strategies by setting a secret reserve price, the proposer is probably better off by publicly broadcasting that it set a secret reserve price as it then has a higher probability of influencing the builders bid. I am not aware of any proposers doing so.

Many thanks to Thomas Thiery and Barnabé Monnot for discussions on this topic.

Ethereum relies on a decentralized validator set to build blocks that uphold chain neutrality. The idea is that transactions one party may censor are not censored by all parties in the decentralized validator set. MEV-Boost uprooted this way of including censored transactions as block building is now primarily done by a small set of sophisticated builders whose preferences for including transactions are not necessarily aligned with the validator’s preferences or network stakeholders broadly.

The min-bid parameter in MEV-Boost functions as a secret reserve price that allows the validator to attach some valuation to its preferences. For example, if a validator has a valuation of 0.05 ETH for building a block themselves, they can set the min-bid parameter in MEV-Boost to this value. The validator then self-builds if the highest bid obtained via the MEV-Boost auction is less than this value and outsources block construction otherwise.

If we assume validators do not censor transactions, then allowing validators to express their preferences in this way decreases the delay for censored transactions to be included while allowing validators to benefit from MEV revenue when this revenue is high. This was the original reason why the min-bid parameter was proposed.

The min-bid parameter elegantly balances weak censorship resistance with strong censorship resistance. Weak censorship means all transactions that pay the necessary fees will eventually be included, although certain censored transactions may experience some delay. Strong censorship means censored transactions will never be included. Strong censorship could happen when a minority of validators who do include censored transactions are re-orged out of the chain by the majority of validators. Allowing all validators, regardless of sophistication, to benefit from high MEV opportunities ensures that the validator set will stay decentralized and, therefore, prevents strong censorship. Allowing validators to self-build when MEV opportunities are low increases the network's weak censorship resistance, as censored transactions are included faster.

In practice, the min-bid parameter seems to work quite well. Data analysis by Data Always found a lower bound of 6.5% of proposers using the min-bid parameter. Building on this, 2.65% of all blocks revert to local block building because of min-bid, contributing to about 7% of non-censored blocks in total.

This post explores whether we can make small improvements to the min-bid parameter. The root of its inefficiency is that it is secret. A validator first runs the MEV-Boost auction, and ex-post sees whether the highest bid exceeds the min-bid value. This means that the reserve price does not influence the bids in the MEV-Boost auction.

Let us introduce a little bit of notation and analyze the potential outcomes of the MEV-Boost auction. Let v_max denote the highest valuation for the block amongst all bidders. Let b_max be the bid of the bidder with the highest valuation and assume that bids are non-decreasing in valuation. Let r_min be the reserve price of the validator. We could then end up in three situations

1. v_max > b_max > r_min. The highest valuation and bid are higher than the secret reserve price, and the proposer sells its block-building rights to the highest-paying builder.

2. r_min > v_max > b_max. The highest valuation and bid are lower than the secret reserve price, and no transfer occurs.

3. v_max > r_min > b_max. The highest valuation is larger than the secret reserve price, but the highest-paying bid is lower than the secret reserve price. No transfer occurs.

The secret reserve price is irrelevant in the first case. The second case demonstrates the reserve price's intended use. The third case, however, is problematic. Block-building rights are not allocated to the agent that values it the most, the builder with the highest valuation, but instead to the proposer.

If the reserve price were public, the third case would not occur because the builder with the highest valuation would bid at least the reserve price. If the reserve price is set to how much the proposer values self-building, publicly revealing the reserve price means that the block-building rights should always be allocated to the agent that values them the most. The property of allocating the block-building rights to the agent that values it the most is called allocative efficiency and could be a desideratum of allocation rules.

Now assuming a public reserve price, the expected welfare gain is Pr[Third case] * (v_max - r_min). The problem is that the builder solely realizes this welfare gain since the builder only needs to pay the proposer exactly the value that the proposer assigns to keep the block-building rights. Can the proposer do better and capture part of this welfare gain?

Let v_keep be the value that the proposer assigns to keeping the block-building rights. Up until now, we have assumed that r_min = v_keep, but strategic proposers could set a reserve price that is higher than their actual value r_min > v_keep. Setting a higher reserve price excludes more builders (increases the probability of ending up in the second case) but increases the revenues when the builder with the highest valuation would bid under the reserve price if it were secret (akin to the third case).

It turns out that setting a reserve price that is higher than the value that the seller attaches to the item, r_min > v_keep, can increase revenues under certain conditions. This idea is called the exclusion principle in auction theory. The intuition is that a seller excludes buyers with very low valuations, those whose valuations are lower than the reserve price, but the seller increases revenues when there is a single buyer with a higher valuation. The probability of the former happening is low as all bidders need to have lower valuations than the already low reserve price. The probability of the latter happening is slightly higher because all but one of the bidders must have valuations that are lower than the reserve price, but the valuation of the highest bidder must be higher than the reserve price.

I purposefully avoid attaching any specific model to this because the MEV-Boost auction is a complicated auction that somewhat resembles an English auction. However, it is also time-constrained, has no perfectly competitive market, and the interdependencies between builder valuations vary over time. This post aims to raise the idea that the exclusion principle can be used in MEV-Boost, not to propose an optimal way of setting reserve prices.

One could argue that publicizing the min-bid parameter decreases the network's weak censorship resistance. While it is likely that fewer blocks revert to local block-building because of a public reserve price, this only happens in very few blocks anyway. Moreover, I believe we should not celebrate the third case presented above because neither the proposer nor the builder is happy with the outcome.

If strategically setting reserve prices increases expected revenues, then more proposers will use the min-bid parameter. Although the expected revenues are higher, a higher reserve price will also lead to more locally built blocks; hence, in equilibrium, the number of locally built blocks may actually increase while we rely on altruism less.

Implementing public reserve prices could be very straightforward. The simplest way would be for proposers to message builders or relays with their reserve price. Relays could choose to enforce the reserve price or not. If relays do not do so, builders may doubt the credibility of the reserve price, decreasing their bids. A proposer may still accept a builder bid below the public reserve price they broadcast if they wish to do so according to a private min-bid value. If relays do enforce the reserve price, credibility is not so much a problem.

Finally, relays could implement entry fees, a fixed and nonrefundable amount that bidders must pay to the auctioneer to be allowed to place a bid. Auction-theoretically, this is similar to setting a reserve price. Bidders with very low valuations are excluded, while those with higher valuations pay slightly more. Relays could help users strategically set entry fees or reserve prices and share the profit. This could be a way to monetize relays.

As an example, proposers could privately communicate their true value for locally building a block to the relay. This value could be zero. Then, the relay suggests a strategic reserve price that the proposer could publicly broadcast through the relay. If the highest bid is indeed the reserve price, the proposer and relay could share the difference between the strategic reserve price and the true reserve price of the proposer. Similarly, the relay could strategically set an entry fee based on the proposer's true value for building the block locally, and the proceeds of the entry fee could be split between the proposer and the relay.

What the equilibrium effect of publicly broadcasting min-bid on censorship resistance is is difficult to ascertain. This post does highlight a potential way for sophisticated proposers to extract more MEV than less sophisticated proposers which is bad for strong censorship resistance. Relays could take the burden of this sophistication, potentially increasing the viability of neutral relays, but also increasing their importance in the ecosystem. Finally, fewer blocks will revert to local block building for proposers currently using the min-bid parameter and who will set a public, not but strategic, min-bid. However, potentially, more blocks will revert to local block building for proposers that will set a public reserve price in order to gain more revenues but currently do not use the private min-bid parameter.

If you want to implement public reserve prices into mev-boost or a relay, please get in touch with me!

P.S.: In this note, we have assumed that secret reserve prices are not considered in builders’ bidding strategies. Since only 6.5% of proposers reportedly use the secret reserve price, I believe this is a fair assumption. Moreover, if it is a proposer’s goal to increase revenues by influencing builders’ strategies by setting a secret reserve price, the proposer is probably better off by publicly broadcasting that it set a secret reserve price as it then has a higher probability of influencing the builders bid. I am not aware of any proposers doing so.