A segment of the Bitcoin community is preparing a user activated soft fork (UASF), using Bitcoin Improvement Proposal 148 (BIP148). If they go through with it, there could be two types of “Bitcoin” on and after August 1st, which this article will refer to as “148BTC” for the BIP148 side of the split, and “LegacyBTC” for the non-BIP148 side.

At time of the split, 148BTC nodes will no longer recognise the LegacyBTC chain as valid — no matter how much hash power mines on this chain. 148BTC would basically just be its own coin.

But the opposite is not true. Because BIP148 is a backwards compatible soft fork, LegacyBTC nodes will recognise the 148BTC chain as valid if it ever becomes the longest chain (that is, most total proof of work). Once this happens, the entire LegacyBTC chain since the point of split would be “re-orged” away: it would disappear. Then only the 148BTC chain will be left, which this article will refer to as “UnifiedBTC.”

What follows is an examination of the scenario of the BIP148 soft fork under a set of four starting assumptions. And: an explanation of why the game theoretical implications of this scenario suggest that rational miners will activate SegWit through this soft fork.

The Starting Assumptions

This is not the type of article that examines all possible scenarios of the BIP148 UASF. These scenarios are plentiful and as varied as the human imagination.

Instead, this article takes four presumably reasonable starting assumptions and draws the single most likely scenario from there.

These starting assumptions are:

1) BIP148 does get activated, and at least some hash power is attributed to 148BTC no matter what. Or, more specifically, enough hash power is dedicated to this chain to eventually reach the point where mining difficulty is re-adjusted to normal, two-week levels. This is a strong commitment, but keep in mind that almost any amount of hash power would eventually reach this point, while producing hash power becomes cheaper over time.

2) All else being equal, the market would value 148BTC (or UnifiedBTC) more than or equal to LegacyBTC. In other words, if hash power, re-org risks, or related considerations played no part, the market would prefer a bitcoin that has SegWit activated through BIP148 over a bitcoin that does not. Or at least, the market wouldn’t mind it if a bitcoin had SegWit activated through BIP148, and would value it equally to a bitcoin that does not. (This includes a bitcoin that has SegWit activated through a different activation method later on.)

3) Both the market and at least a majority of miners (by hash power) behave in a rational, profit-maximizing way and have sufficient information to do so.

4) There is no hard fork, counter soft-fork, checkpoint or anything like that on the LegacyBTC side of the split. This would equate the creation of a new coin, and just make it so that users and miners can pick and choose as they would among altcoins. That being said, even in most of these cases the game theory described in this article still holds up. (Notably, Bitmain’s claimed “contingency plan” would ensure that it holds up stronger.)

Interestingly, not all of these starting assumptions even need to be true. In the style of a Keynesian beauty contest, it’s actually enough if a majority of miners (by hash power) thinks they are true, or if they think that other miners think they are true, or if they think that other miners think that other miners think they are true… and so on.

It should also be noted that this article omits some nuance; for example, regarding potential hash power attacks, fee levels on different chains, pruned nodes, a possible AsicBoost advantage, or developer support. While all this may skew miners’ behavior to some extent, none of it should fundamentally change the dynamic described here.

The Market’s Options

More than anything else, bitcoin gains value from holders: the people and entities that accept bitcoin in trade and hold on to it as a store of value. This also includes miners after they’ve mined new bitcoins and hold on to them, which Bitcoin’s protocol rule forces them to do for at least 100 blocks after the coins have been mined.

Once the UASF is activated on August 1st, all holders will have a choice of three options:

1) 148BTC or UnifiedBTC

2) LegacyBTC or nothing

3) Both 1 and 2

Option 3 will mostly represent holders who don’t send or receive any coins until the situation is resolved. This has no bearing on the game theory of a BIP148 coin-split, so we’ll ignore this option.

The other two options, 1 and 2, may seem strange to you. You may have thought that there will simply be a choice between LegacyBTC and 148BTC in much the same way the Ethereum split simply resulted in a choice between ETH and ETC. But that’s not the case.

This is because if you choose to hold 148BTC, should a re-org happen at any time in the future, you will instead be holding UnifiedBTC.

On the other hand, if you choose to hold LegacyBTC, should a re-org happen, you’d find yourself holding nothing at all.

So holders really have the option between “batches” — not just two types of bitcoins that happen to exist at a specific point in time.

‘148BTC or UnifiedBTC’

When BIP148 activates, under the stated assumption, at least some hash power will be attributed to 148BTC. This could be very low compared to LegacyBTC: perhaps 10 percent, perhaps 1 percent, or perhaps even less. But no matter how low the hash power is, 148BTC will then “exist.”

Now remember that, all else being equal, 148BTC — or UnifiedBTC — should be worth more than LegacyBTC, or at least as much. The market will prefer a bitcoin that has SegWit activated through BIP148 over a bitcoin that does not.

From a pure, trading perspective, then, it’s easy to see why it will make sense to invest in 148BTC at any price lower than (or equal to) LegacyBTC, especially if you’re buying 148BTC with LegacyBTC. If 148BTC trades at a mere percentage of LegacyBTC’s exchange rate, it could potentially offer a 100x return on investment.

Of course, in reality, not all things are likely to be equal. Most importantly, 148BTC may find itself with much less hash power support, which will result in lower utility (slow confirmation times) and lower security (cheaper to perform 51%-attacks).

Nevertheless, keep in mind that this means that low hash power is the main reason why this investment case may not hold up.

Hash Power and Value

In a normal situation, where miners act as rational profit-maximizing entities, hash power tends to follow price. Miners want to make as much money per hash as possible, so they mine the most profitable coin. If a coin gains in value, more miners will point their machines to this coin. When a coin loses value, miners will increasingly switch to another coin or turn their machines off completely. This is clearly seen in the altcoin markets, for example.

However, this coin-split scenario is not a normal situation. Under the stated assumptions, the main reason 148BTC won’t be valued as much as LegacyBTC, is that it may not have as much hash power.

But this means that an increase in hash power should also increase 148BTC’s price.

And that makes intuitive sense. If 148BTC goes from 0 percent of total hash power (between 148BTC and LegacyBTC) to 1 percent, it improves from “unusable” to “more than one set of transactions per day”: not unlike typical fiat transfers — just less of them. At 15 percent hash power, SegWit will activate before the timeout of November 15th, further increasing utility. And at 33 percent, LegacyBTC miners can no longer 51%-attack the 148BTC chain without re-orging the LegacyBTC chain away. Increased hash power would likely increase 148BTC’s price.

Moreover, with only 51 percent of total hash power, 148BTC turns into UnifiedBTC and will therefore account for 100 percent of total value. This suggests that a single percentage of hash power increase would, on average, increase 148BTC’s price by more than a percent.

And the opposite is just as true.

If LegacyBTC ever drops a single percentage from 50 percent of total hash power to 49 percent, it will (eventually) turn into “nothing,” and its value will drop significantly: to zero. By extension, if LegacyBTC ever decreases from 51 percent to 50 percent of total hash power, it should increase the risk of this scenario playing out, which should also decrease its price. And that should also be true for any hash power decrease.

This is important because it flips the normal situation, where hash power mainly follows price, on its head. For 148BTC, increased hash power should further increase price. While for LegacyBTC, decreased hash power should further decrease price.

Game Theory: A Primer

The basic idea behind game theory is that rational players in a game can anticipate the moves of other rational players and make the best mathematical decisions accordingly.

As a simple example, let’s say Alice auctions off a dollar to Bob and Carol. (And for those well-versed in game theory, don’t confuse this example with the better-known and paradoxical dollar auction; we’re keeping it simple here.)

Bob is first to bid, and could bid 1 cent to win a grand total of 99 cents. But of course, Carol could then outbid Bob for 2 cents. Then Bob and Carol could go through the motions of bidding 3 cents, 4 cents, 5 cents… up until one of them bids 99 cents. It makes no sense to bid a dollar for a dollar, while it always makes sense to outbid your opponent up until 99 cents, so 1 cent profit is the maximum each can win.

Now, if Bob and Carol are both rational, they both already know they could win the maximum if they’d just bid 99 cents straight away: they know that’s what they should do if they want to win the maximum. Moreover, if Bob gets to act first, and he knows that rational Carol will bid 99 cents on her first turn, Bob definitely needs to bid 99 cents, or he’ll lose out on his cent.

The important takeaway is that because Bob can anticipate the outcome of a bidding race, and assumes Carol can too, there would be no bidding race. Bob would end the auction with one bid.

BIP148’s Game Theory

Not unlike Bob and Carol in Alice’s auction, rational bitcoin miners can anticipate how other rational bitcoin miners as well as rational bitcoin markets will act after the BIP148 split … in order to prevent a split.

Let’s say the market initially expects 148BTC to gain only 1 percent of total hash power. 148BTC currently doesn’t exist yet, so that would basically be an increase from zero to one.

Now, remember that for 148BTC, increased hash power further increases price, while for LegacyBTC, decreased hash power further decreases price. So if one percent of total hash power were to mine 148BTC, the market should (eventually) push the price of 148BTC higher than 1 percent of the total. Meanwhile, the market should also (eventually) push the price of LegacyBTC down to below 99 percent of the total.

But of course, if the market now expects 148BTC to (eventually) have more than 1 percent of total price, miners should also be expected to (eventually) dedicate more than 1 percent of total hash power to 148BTC, and less than 99 percent to LegacyBTC. After all, hash power also follows price. It always does.

And yet again, if the market expects 148BTC to (eventually) have more than 1 percent of total hash power, this should drive the expected price up even higher. And it should push the expected LegacyBTC price even lower.

As a result, we’re in a situation resembling Bob and Carol’s bidding race. 148BTC’s expected hash power increases 148BTC’s expected price … which increases expected hash power, which increases expected price. The exact opposite is true for LegacyBTC.

This can ultimately only lead to one conclusion. Both rational markets and rational miners should expect 148BTC to eventually be the only coin standing, as UnifiedBTC.

Now, if miners expect only UnifiedBTC to be left standing eventually, it is of course smart to switch from LegacyBTC to 148BTC before other miners do. And if all miners know that all miners know this, and all miners know that all miners know this, they have only one rational decision to make. Like Bob in Alice’s auction, miners should switch to 148BTC immediately.

Moreover, knowing that all rational miners would switch to 148BTC immediately makes it even more irrational for any individual miner not to switch immediately. He’d be wasting hash power on blocks that would be rejected — orphaned — by other miners.

That is, of course, if miners think the stated assumptions hold up.

Am I wrong? Feel free to let me know via email at aaron@bitcoinmagazine.com or on Twitter at @AaronvanW