Segwit2x Game Theory Scenarios Part 1

The Segwit2x hard fork is coming in less than two weeks and many are wondering about what may happen. In this article, I’m going to go through a few of the scenarios. Big caveat is that I don’t expect any of these scenarios to come to pass. We are examining first-order scenarios in order to examine more complicated scenarios in a later article.

Current Situation

The current situation is the culmination of a lot of events that have come before which include the following:

• November 2015 — Pieter Wuille presents the Segwit proposal
• February 2017 — Shaolinfry proposes UASF
• March 2017 — UASF becomes BIP148
• May 2017 — NYA is signed
• July 22, 2017 — BIP91 goes into effect
• August 24 — Segwit activates

The btc1 repository hard-coded the fork date to be 90*144 blocks after Segwit activation. This block, 494784 is estimated to be around November 15–16.

What happens at this block is the main point of interest today.

Scenario 1: 2x is abandoned

The easiest scenario to analyze is where the New York Agreement signers decide collectively to not fork at all. In this scenario, all the miners, merchants, wallets and services that entered into the agreement collectively decide to reverse course and not run the 2x software at block 494784.

The 2x hard fork then would not occur as no one would mine a block with larger than 4,000,000 block weight. A single chain results.

This is the least disruptive scenario, but is improbable for a number of reasons. First, a single miner supporting the 2x hard fork can make the fork actually happen. A unanimous abandonment of 2x would have to occur. The fact that ViaBTC was able to single-handedly hard fork Bitcoin to produce Bitcoin Cash shows that a single motivated miner can cause a fork. Second, this requires the entirety of the NYA to be abandoned at once. Given how close we are to the actual fork, this would be a massive credibilty hit and is unlikely to occur for that reason.

Because unanimity among a very diverse set of miners is required, this scenario looks pretty unlikely.

Scenario 2: Core capitulation

In this scenario, we assume that a lot of Core devs have a change of heart and start recommending upgrading to 2x last minute. Even in such a low-probability scenario, there will be nodes that don’t upgrade to 2x. Such nodes will stall out at block 494783 and will wait for someone to mine the next block.

Perhaps if a lot of Core devs recommended 2x last minute, many would listen. However, some will not and the question here is will there be miners that would still mine the legacy/1x/non-upgraded chain. Again, much like the previous scenario, a single miner can cause a second chain.

This is a very low-probability scenario, even lower than the previous scenario, as so many Core devs have come out against 2x. Such a sudden change of heart likely will be seen as some sort of coercion and not genuine and will likely result in a continued legacy/1x/non-upgraded chain.

Scenario 3: 2x miners honest, no attack

In this scenario, miners stick to the New York Agreement, possibly mine at a loss and create a giant asymmetry in hashing power in favor of 2x.

The proportion of miners signaling NYA has fluctuated from 85% to 95% over the past 3 months. We’ll pick a number in the middle and say 2X has 90% of total hashing power. We also assume that the miners signaling for NYA means they are committed to mining 2X in perpetuity.

That means 1X will have 10% of the block hashing power of 2X. 1X will have blocks 494784 onward take 10 times the normal amount of time on average. That would mean 100 minute blocks. We assume in this scenario that the higher hash power chain does not attack the lower hashpower chain and that the hash power proportions remain the same.

The events from this point on go something like this:

• November 15, 2017 — Block 494784 splits to 1X and 2X. Initially, 1X has 100 minute blocks, 2X has 11 minute blocks on average. 1X and 2X have the exact same difficulty.
• November 24, 2017 — Block 495936 is mined on 2X. 1X continues to have 100 minute blocks, 2X now has 10 minute blocks. 2X is now 9% easier to mine than 1X.
• February 3, 2018 — Block 495936 is mined on 1X. Difficulty retargets downward by a factor of 4. 1X has 25 minute blocks, 2X continues to have 10 minute blocks. 1X is 3.6 times easier to mine than 2X.
• March 10, 2018 — Block 497952 is mined on 1X. Difficulty retargets downward by a factor of 2.5. 1X has finally adjusted enough to mine 10 minute blocks, 2X continues to have 10 minute blocks. 1X is 9 times easier to mine than 2X.

These are rough estimates, but we can see that both chains will more or less be normal in 4 months. More hashing power on 1X makes the difficulty adjustment come faster (15% means block 495936 occurs on Jan 1 instead of Feb 3, for example) and less hashing power on 1X makes the difficulty adjustment come slower (5% means block 495936 occurs on April 24 instead of Feb 3).

Futures markets are currently predicting something like $1100/B2X coin and $6100/B1X coin. Assuming this price is predictive, there will be some massive opportunity cost for anyone mining 2X. The opportunity cost per block will get 3.6 times bigger after block 495936 (Feb. 3) when it will be 3.6 times easier to mine 1X. After block 497952 (Mar. 10), the opportunity cost per block will be 9 times bigger than was on block 494784 (Nov. 15).

In order to motivate miners to stay on 2X, there has to be some reward that is at least as much as the opportunity cost. We can estimate the opportunity cost based on the current futures prices. The opportunity cost is ($6100-$1100)* 12.5 per block before block 495936 (Feb 3) or $62,500. That amounts to something like $9M/day.

These calculations assume a static prices for both B2X and B1X and miners are most likely counting on that number changing. Each B2X token has to be worth 1 B1X token in order to reach profit parity, which is something like 6x increase in the B2X token relative to the B1X token.

A better price for 1X makes the opportunity cost go up. A $6500/$650 price for B1X/B2X makes the opportunity cost go to about $10M/day. A worse price for 1X makes the opportunity cost go down ($5000/$2500 implies a $4.5M/day opportunity cost, $4000/$3000 implies a $1.8M/day opportunity cost)

Futures markets are just about the only objective indicator here and they seem to indicate that this scenario will have an astronomical cost, something like $1B if prices/hash rates stay static over 4 months.

This is not economically stable and something has to give in this scenario. There are four ways in which economic stability can be reached:

1. Price follows Hash Power — The price of B2X coins goes up a lot (around 36x), the price of B1X coins goes down a lot (around 1/36) or some combination thereof.
2. Hash Power follows Price — Hash power moves from B2X to B1X (Something like 75% of total hash power moves from B2X to B1X)
3. Massive Dollar Injection — B2X is bought with outside money and causes it to go up (around 36x), B1X is short sold with outside money and causes it to go down (around 1/36 of before) or some combination thereof.
4. Massive Hash Power Injection — New hash power is brought into B1X.

Most likely some combination of the above will happen to fill the obvious economic gaps.

Conclusion

A static, first order estimation of the current situation suggests that the current futures market price and current mining split is not stable economically. The people on different sides of the debate essentially stand on different sides of what will correct.

In other words, the current projection requires some change in either price or hashing power to become stable. Next time, we’ll go through second order scenarios that result from each parties’ knowledge of the these scenarios.

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