Thoughts on Drivechain II: How bad is MEV?

Some suggest MEV will lead to miner centralization. Centralization is always a major concern, and anything that potentially adds nonlinearities in returns for miners needs to be watched closely .

At first glance, it’s not obvious that sidechain MEV will pass through to L1. If the L1 miners are just accepting competitive bids, the MEV seems to have no way to pass through and distort incentives of L1 miners.

But what jumps out at me, having thought about it for a bit now, is that the nature of BMM (unlike Nakamoto consensus) in general is conducive to anti-competitive practices by miners, perhaps first on the sidechain, then on the main chain. The concern is that miners on the sidechain will not be content to fight one another for tiny margins, and use the auction mechanism to eliminate competition. This invites L1 miners to step in and behave in similar ways. This then leads to soft-core collusion among the L1 miners for sidechain revenue, without immediately disrupting the main chain. The problem is that this does give advantage to larger miners, possibly resulting in smaller miners being pushed out and the larger miners gaining more share.

In general, the BMM auction model is not great, the finality provided is horrible compared to Nakamoto consensus (essential linear vs exponential) so I don’t actually think serious projects with serious MEV would use BMM in the first place.

There’s a number of reasons a serious decentralized project would stay away from BMM:

1. Decentralization is largely pointless; anybody can effectively censor the network by promising to supplant any block by outbidding to replace any block with an offending transaction. If the threat is credible (credibility is easy to establish— just follow through once or twice) the transaction is essentially censored.
2. Chainsplit ties are not resolved by randomness, but by signaling/bluffing, dollar auction games, and coalition-forming. So if there’s a dispute - you want to make sure you’re on the right team, or at least are not working against the wrong team.
3. Block creation requires zero investment in the sidechain. Unlike PoW which requires hardware or PoS which requires investing in the tokens: With BMM anyone can come in off the street, buy some L1 token and start creating blocks, which may or may not even be valid.
4. With 3) in mind, any outside mercenary can perform extortion on any users of the sidechain, or can simply go after the sidechain if they have some way to profit by trashing the sidechain. (If there’s some basic protection against this in the protocol, let me know, I haven’t seen this, other than “miners won’t let this happen.”)
5. Because the finality is more “linear” than “exponential” there might be several chains that are viable at one time. Being the shortest chain by 12 blocks only means someone has to outbid 20 out of the next 27 blocks. In Nakamoto consensus a chain 12-blocks-uncle’d is ancient history. If there is a volatile asset or futures contract recorded a sidechain, it might make sense for a heavy player to keep multiple viable chains alive.
6. There can be really weird dynamics and rules around soft-forks. Instead of miner signaling for a fork or a UASF you also have Highest Bidder Activated Soft Fork. Someone can just declare a soft fork, and then outbid to supplant blocks that don’t comply with the new soft fork rules.
7. Be creative — if all you need is a little money to there’s a lot of fun shenanigans available that are simple not available with PoW or PoS

MEV, though

First, we should clarify that there’s 3 categories of MEV.

Type I. MEV that happens within a block and is available to anybody who mines that single block with a reasonable amount of capital and computing power to identify it and execute on it.

Type II. MEV that occurs when mining multiple blocks in excess of the blocks mined independently.

Type III. MEV that becomes available only to larger well-resourced parties or collusive miners.

Another interesting category of possible miner revenue, especially in BMM, is snipe-able revenue. This differs slightly because typically this involves miner stealing directly from each other rather arbitraging opportunities from the general ecosystem.

Part of the problem with the discourse is these are sometimes combined. Type I can be in some situations be relatively benign and is probably the majority of MEV — yet sometimes the volume of occurrence Type I is used to suggest the more harmful types of MEV also occur in abundance, but this isn’t clear.

To set up terminology, we distinguish the two types of miners: L1 miners (L1M) are the standard bitcoin miners, who mine blocks while accepting bids the SC blocks. We will call the sidechain miners “sidechain virtual miners” (SCVM). Obviously any miner could be both.

Claim 1. In the absence of L1M acting as SCVM, the sidechain is likely to develop anti-competitive behaviors.

Drivechain advocates have put forward a somewhat simplistic model which suggest that SCVM will engage in a stiff competition for very small profits. If the total revenue available to SCVM is $1000 to mine block D+1, the bids will come in at $950, $990, $995 etc, passing nearly all the revenue onto the L1M.

However, the auction nature of BMM suggests SCVM miners will not be content to compete for 1% of the revenue. Competition is for losers. It’s more likely they will engage in anti-competitive signaling or explicit collusion, or some combination of both.

To begin, immediately one should agree that nobody would pay $950 for $1000, if there is only a 90% chance of collecting the $1000. So a smart and aggressive SCVM will occasionally outbid the previous block winner. This is easy to do with BMM, you simply bid for the previous block instead of the next one. The previous block winner can then directly engage in a war of attrition as the bully SCVM builds on their own fork, or they can bow out. It’s stupid to engage in a long type of war of attrition, which is essentially a dollar auction. With proper signaling this will end quickly. Now it’s established that there is a positive probability that some blocks might be lost. This drives the bid price down.

This doesn’t have to be just pointless acts of theft, this can happen due to fee-sniping opportunities presented by revenue variability. If the revenue for block D is $1000 and the revenue for block D+1 is $800, the aggressive SCVM will go after block D, if they don’t already have it. So, unless you want to challenge the aggressive miner, you don’t want to bid more for block D than you expect to be available for block D+1, as this opens you up to sniping.

This discussion so far is basically only for Type I, but it becomes massively worse with type II. If the revenues for blocks D-2, D-1,D and D+1 are all $1000 respectively, but a well-resourced SCVM can recombine the transactions in all of them to gain $10,000, and they can signal this is their intention, they can just go ahead and do this. They will spend much more than other miners who are bidding on chaintip blocks.

Quickly, this gets into games of signaling and coalitioning. Knowing they are going to win a pissing contest, aggressive SCVM might aggressively supplant 5%, 10% 15% of weaker players blocks, further driving bidding prices down and eliminating competition. Now there could be multiple such players, but they would quickly come to some arrangements. Larger SCVM may agree to not engage in wars of attrition with other large SCVM, or they could all combine forces to become a single monopoly SCVM (publicly, or perhaps via secret agreements.)

Note that the SCVM monopoly is incredibly easy to enforce — every time some upstart miner outbids you, you simply outbid them, and then follow that with more bids, it will be a waste of money for the upstart, who paid good L1 bitcoin to get their block accepted.

The motivation to monopolize is huge: Instead of competing, paying $995 for $1000, you can now take most of the profit — you only have to pay standard UTXO fee rates, this might mean you pay $50 or $100 to claim the $1000. Huge profits.

Where are the L1 miners in all of this? They don’t care. They’re accepting the highest bid. Maybe some do care, but they’re fighting a losing battle if they chose to accept smaller revenues from “honest” or “competitive” SCVM that will eventually just get stolen by the anti-competitive SCVM. It’s a tragedy of the commons situation — each time an L1M accepts a large bid from the monopolist, they doom future L1M to less revenue.

Claim 2. If SCVM are behaving anti-competitively, L1M will mine sidechain blocks as well.

Clearly, the miners realize they are missing out of large revenue streams if the sidechain is being mined by monopolistic SCVM. Unlike an SCVM who would challenge the monopolist, the L1M have different cost considerations: If they win a block they get to decide, they don’t have to outbid. The cost of claiming the block is only the opportunity cost of the monopolist’s bid for that block. Obviously, they can choose to ignore bids by the SCVM that are anti-competitive.

Now as before, the bully SCVM may attempt to punish the miners by putting in a bid that is higher the block reward, but this now a slightly different situation. It’s more costly for the SCVM to persist in this, because each time they must beat the full revenue in the block, not just the highest bid.

It seems like a reasonable and smart Schelling point that miners continue to mine their own SC blocks. This a repeated game, and L1M know that they are much better off not letting the SCVM behave anti-competitively. They may even engage in tit-for-tat strategies in order to stifle an SCVM attempting to punish L1M for mining blocks.

Now for type I MEV with little variation this is probably OK, but it gets interesting if there is significant variation. Suppose sidechain block D recorded on block N and has $1000 in revenue, block D+1
appears to have only $800. The miner of block N+1 has a decision, snipe
the $1000 by mining it (perhaps undercutting slightly) or be content with the $800. One problem with accepting the $800 now is that the next miner, if left with, say $600, may try to go all the way back and mine the $1000 anyways, and then bribe subsequent miners. A key difference here is that L1M can always bribe each other to mine on sidechain forks. To continue this example, if block N contains a $1000 SC block D, block N+1 contains $800 SC block D+1, the L1M mining N+2 might go back and remine D , collecting the $1000, then go ahead and bribe the miner of block N+3 to mine their fork of D+1 (say by paying $800, as opposed to the block sitting there, which might be worth $700) and then bribe the next miner. Once they’ve declared their intentions, other miners just want to be on the winning chain, and happy to accept the bribe.

Now this gets really dicey and hard to model if there is Type II MEV. Again
this falls onto to signaling and bluffing, but the bully has somewhat
less power on L1 because of the probabilistic nature, they are not guaranteed an opportunity for the next block. It’s difficult to model, but one could easily imagine that L1 miners might begin to do some soft-core collusion when mining the sidechain. A few bigger miners
could agree to control the sidechain, and split the profits. They could behave as bullies, bidding with one another to force out the smaller miners when performing fee-sniping on the previous chain. This is
not really affecting the progression of the main chain, it’s affecting the centralization (as a percentage of blocks mined and revenue)
of the sidechain, but again it introduces the opportunity for collusive flirtations. There’s two problems here: 1) the larger miners who are colluding with one another will be generally collecting more sidechain revenue. 2) This could begin a slow continuous path towards more and
more collusion, snowballing into one cartel of miners.

The danger seems not so much in the MEV per se, but the fact that L1M can easily perform all types of sniping by directly winning blocks or by bidding for them, without disrupting the progression of L1. This favors larger miners and miners willing to collude, and could serve as a gateway to more dangerous collusion.

Repeated games have many equilibria

I could be overly pessimistic; It’s a worth-noting fact from game theory that infinite horizon repeated games have infinitely many Nash equilibria. It’s completely possible that L1M and SCVM could settle for a default compliant mining strategies, small but steady profits. But with BMM, it’s incredibly easy for anyone who takes their eyes off the infinite horizon to deviate and create other opportunities. It’s a leap of faith to believe nobody will do this.

Summary

Bitcoin is secure in the near future because the gap between profitable miner misbehavior and default compliant mining remains huge. In order for any deviant strategies such as undercutting to become profitable, many other miners would have to also engage in strategic mining, accepting bribes or choose an undercut chainsplit. But the Schelling point at the moment is to steer clear of this. In general, a culture of collusion and strategic mining is simply not present (for the time being.) Bitcoin becomes insecure when this gap shrinks and miners find if profitable to form coalitions and play around with deviant strategies.

Deliberately remining block N is very risky move on the main chain, you risk losing 100% of the revenue for that block. But with BMM you can remine block D while mining L1 block N+1, you only risk say 5% of your revenue if this goes south.

For this reason, BMM sidechains offer a fertile sandbox for L1 miners to test out all sorts of deviant strategies; fee-sniping, undercutting, bullying, extortion, bribing, all without messing with the main chain. This could provide a series of stepping stones toward this behavior on the mainchain

The issue with MEV is that with BMM, it’s likely that Type II and III will be incredibly abundant, due to the linear nature of finality, leading to ample opportunities to test out deviant mining strategies on the sidechain.