A Deeper Look Into Bitcoin Network Effects
Kyle Samani from Multicoin Capital wrote a thought provoking piece recently On The Network Effects Of Stores Of Value. I highly recommend reading that first and spending a bit of time thinking it through.
Most people generally assume that bitcoin has strong network effects, and that money in general possibly has the strongest network effects of all. The best known rule for how to value network effects is Metcalfe’s Law. Whenever network effects are dicussed Metcalfe’s Law is sure to be mentioned. The law states that the value of a network is proportional to n² where n is the number of participants or nodes in the network. The typical example is the telephone system, where with n participants each can contact the n-1 other participants making the total value of the network proportional to n * (n-1) which for all but the smallest values of n can just be approximated by n².
Kyle has tweeted often that he thinks the network effects for a store of value (SOV) are much weaker than commonly assumed and that rather than n² they are more like log(n) (See ¹ and ² in the footnotes below). By implication he is saying (this part is my words not his) that since bitcoin is gravitating towards being a store of value, the network effects for bitcoin are much weaker than most people assume. This probably sounds a bit mathy and you might be thinking who really cares as long as there are network effects. To get an idea of the difference let’s take a look at growth based on n² versus growth based on log(n). For good measure lets also include linear growth.
Look at how fast network value grows under the n² assumption, and how slowly it grows under the log(n) assumption. Log(n) growth is significantly slower than linear growth, which itself is significantly slower than n² growth. Below is a chart of log(n) growth versus just linear growth. In comparison to linear the log(n) growth looks like a flat line at 0.
One way to tell if network effects are at play is to look at the number of providers in an existing market and how dominant the lead provider is. If there are strong network effects then you would expect one dominant provider. Network effects lead to winner takes all markets, since the value proposition of the largest provider is so much higher than for anyone else. If a market has strong network effects then it makes sense to get early growth at almost any cost. Once the network effects kick in it will then be impossible for anyone to catch up and the cost incurred to get early growth will be have been worth it and lots more. We’ll come back to this later but for now back to bitcoin.
Kyle convincingly argues that for a SOV your only real concern is being able to get liquidity in the future, for example when you decide to cash out or buy something. So the value to you as each new participant joins is only the extra liquidity they bring, and past a certain point of critical mass the marginal new liquidity as new people join really makes no difference to you.
I agree with Kyle that if liquidity is the only consideration, then the network effects are indeed weak. I can’t help thinking though that there is something more. As each new participant joins the bitcoin network, I also benefit because I can now possibly transact with them without needing liquidity. There is a chance that the other party will accept my bitcoin directly without me needing to convert them into fiat at all. So once enough people are using bitcoin as a SOV, a new benefit emerges whereby we can all transact with each other in bitcoin. You could argue that this is no longer SOV and we are now talking about the medium of exchange role of money where network effects are stronger. This argument is probably correct, yet it does illustrate that there is a natural progression from SOV to medium of exchange once a critial mass of people are using something as a SOV first. The value of this natural progression is not reflected in the log(n) hypothesis. The progression might only start to emerge once there is a large enough critical mass of participants (say 1 billion). So it might not be visible for a very long time (years or decades) and then happen very quickly. Another way of saying this is that for a SOV that is not also a medium of exchange liquidity into the medium of exchange is a significant driver of network value. But beyond a certain point the SOV will start to become a medium of exchange and so the network effects change ⁶.
If we look at the history of money, there tends to be one dominant SOV at any point in time (and for a particular geography if that geography is isolated). This would imply that there might be strong network effects for SOV, but that’s inconsistent with Kyle’s argument that SOV network effects are weak. So why then is SOV a winner takes all market. Network effects aren’t the sole reason for a dominant provider, so let’s try and identify some other reasons why we only tend to see a single dominant SOV at a time. I think there are two simple but powerful reasons:
- People will select a SOV based on the properties of that SOV and the properties of the alternatives available to them. This is not a network effect, but will lead to a majority eventually choosing the same SOV as the market establishes over a period of time which one has the best properties ³.
- There is no need for more than one SOV. Once you have a single SOV with the desired properties the market need for this economic good is now completely satisfied. The only reason for a new SOV to emerge would be if the properties of the current one were compromised or one with better properties came along.
If all of the above is correct (including Kyle’s log hypothesis for SOV), then it also implies that while a new SOV is being established there is no need to rush. It’s much more important to ensure that the SOV has the right properties, even if that takes time and means you get less adoption initially. If the network effects for SOV were strong then this strategy might not be an option, and you would need to hurry and get adoption as quicky as possible even if that meant sacrificing some of the desirable properties for a SOV.
One counter argument is that since the network effects for the medium of exchange role of money are strong, the route to becoming a dominant SOV is to first become a dominant medium of exchange. If people are using you for exchanges then you will become a SOV too. In this case fast early adoption would be important. My personal view is that this is the wrong way around. If you try and become a medium of exchange prematurely, then why will anyone accept you for exchanges (you don’t yet have established value in the market for a large number of people). At best if you are accepted in exchanges then you will immediately be exchanged for something else that does have established value for the recipient. So you end up becoming a payment rail for something else that has value. VISA and MasterCard are used for exchanges all the time (since they are fast and convenient) but the underlying value being exchanged is fiat and not VISA or MasterCard. They are payment rails for facilitating exchanges, which is valuable in itself and their businesses have very strong network effects, but VISA and MasterCard have not evolved into their own SOVs. If Visa and MasterCard released their own token, would that suddenly become a SOV or would it just be a new way to facilitate their service as a payment rail for fiat. Ripple also comes to mind here. They have made many SOV “compromises” in order to facilitate fast and cheap exchanges. How likely is it that XRP becomes a real medium of exchange (as opposed to a payment rail) and SOV. My contention here is that you can’t be a medium of exchange unless you are a SOV first ⁵. First comes value, then comes the exchange of value.
Another possible scenario is that one or more large existing assets will anyway become convenient SOVs once they are on a blockchain, and that those will then be used by the market for exchanges. In this scenario you won’t need a seperate SOV like bitcoin at all. Let’s say I have shares of Apple in my portfolio and those shares exist on a blockchain. I can then just use my wallet to send someone a small portion of these shares as payment. Why do I need another SOV, especially one that’s not backed by a “real” asset such as Apple shares. The reason I don’t believe this will happen is that most people won’t want Apple shares as payment. They will want something else. This is the coincidence of wants problem that money solves and it will still exist when everything is on a blockchain and can be exchanged quickly and cheaply. Money is essentially the single asset that everyone is prepared to accept for exchanges. Ok well what if my wallet instantly converted my Apple shares into something else that the other party will be happy to accept. Again the issue is what is that something else that the other party will accept. There will still be a need for money, the single asset that everyone will accept for exchanges. The demand for how big a balance of money people will want to hold may well change (down or up) but money will still be needed.
Let me end by saying that the above are my strong convictions weakly held. This is a huge economic and social experiment and we will have to see how it turns out. My main arguments are that network effects for SOV (and thus for bitcoin as it exists today) may be weak, but that does not mean SOV won’t be a winner takes all market. The way you win as a SOV is by focusing on having the right properties rather than making compromises for fast adoption. Once enough people are using you as a SOV then the medium of exchange role will start to emerge. Finally if you become a dominant medium of exchange you might then be used as a unit of account (the final role of money). Bitcoin might never get past the SOV role (and that would still be ok), but if it becomes a widely held SOV then it’s also likely to become a medium of exchange next (maybe first for a “local” economy like the internet or a specific online market ⁴), and then one day maybe even a unit of account.
Footnotes
¹ An interesting exercise is to try and understand why log(n) is an appropriate function for weak network effects. One possible explanation is to assume that the 1st new participant adds a value of 1, the 2nd adds only a value of 1/2, the 3rd a value of 1/3 and so on (Zipf’s law). If you take the sum of these values up to all n participants, then that is very roughly approximated by log(n)
log(n) ~ 1 + 1/2 + 1/3 + 1/4 + ... + 1/(n-1) + 1/nSee https://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong for more detail on this and a brilliant explanation for why Metcalfe’s law is too generous.
² Another model for how the value added by each additional participant might drop off over time is as follows.
1 + x + x² + x³ + x⁴ + … (where 0 < x < 1) The value of this sequence for n participants is (1–x^n) / (1–x). If x = 0.99 for example then each additional participant is worth 1% less than the participant before them. The 1% drop off in value each time compounds in a similar fashion to compound interest. Let’s call this “geometric drop” and compare it to log(n).
As you can see on the chart the growth assuming geometric drop is initially much stronger but then levels off quickly (although at a higher level than for log(n) growth). This might be a better or at least an alternative model for weak network effects where the initial participants add a lot of value but after a point of critical mass the marginal value of new participants is very low. It’s also intuitively easier to reason about and you can use different values for the drop off depending on the market. That said I think the most important aspect is whether the growth is superlinear or sublinear and not worrying about the exact function to use.
³ For a discussion on what properties make a good SOV see https://www.amazon.com/Bitcoin-Standard-Decentralized-Alternative-Central-ebook/dp/B07BPM3GZQ
⁴ You could argue that bitcoin is already a medium of exchange and unit of account for crypto traders
⁵ What about compromising a bit on the SOV properties in order to get initial growth and use as a medium of exchange, and then hope that the market feels your SOV properties are good enough, or you try fix up the compromises later. Maybe this is the bitcoin cash approach and it will be interesting to see how it develops.
⁶ Another possible network affect is that I am more likely to consider something a SOV if lots of other people consider it a SOV. So each new participant adds to the social validation.
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