Crypto economy complexity

How to predict when cryptocurrency hard forks and token competition will destroy value

“men err in their productions, there is no deficiency of demand” -David Ricardo

All parties involved in an ICO have a strong incentive to trust in the success of the venture. Technologists care about innovation and long term value, organizers care about maximizing visibility while minimizing regulatory exposure, and retail investors want to get rich fast. Algo traders can profit from the volatility premium in a sustained basis only if they are good at pricing risk, and for this, they need to quantify the relative strength among tokens and the changing prospects for reserve currency status of forked coins. The real reason why large investors get involved is to move money across borders through the path of lowest friction (compared to the alternatives of venture capital, private banking or over-the-counter trading), but even them will sleep better at night if they can trust that the funding team has a real roadmap to value.

But crypto economies are so new — there is little clarity on how competition really works and when value is at risk. In the words of an industry observer, Lex Sokolin: How can something divide, and both parts become greater than the whole, especially when network effects are in play? Shouldn’t all non-Bitcoin altcoins that compete for the same use case go to zero?

I present here a behavioral finance view on crypto economic markets, based on first principles.

The motivation for this approach is two-fold. Quantitative behavioral finance deals with finding factors that can tell us something about the fear, greed, or expectations of economic actors engaging in financial activities. And economic complexity matters because it helps explain differences in the level of income of whole economies, and more importantly, because it predicts future economic growth.

We demonstrate that attention flows manifest knowledge, and the distance (similarity) between crypto economies has predictive power to understand whether a fork or fierce competition within the same space will be a destructive force or not.

The micro view: Coase’s Theorem

When dealing with hundreds of currencies and thousands of tokens investors have to face a very practical constraint: attention quickly becomes a scarce resource. To understand the role of attention in trustless markets we should turn to the work of Ronald Coase, the Nobel laureate, who demonstrated how it is possible to trade on an externality or “social cost”. For the theorem to hold, the conditions that the crypto communities that will split should meet are:

Well defined property rights: the crypto investor owns his attention.

Information symmetry: it is reasonable to assume that up to the moment of the hard fork market participants are at a level ground in terms of shared knowledge. Specialization (who becomes the expert on each new coin) will come later.

Low transaction costs: Just before the chains split there is no significant cost in switching attention. Other factors (such as mining profitability) will play a role after the fact, and any previous conditions (e.g. options sold on the future new coins) are mainly speculative.

The condition of symmetry refers to the “common knowledge” available at t-1 where all that people know is the existing coin. Information asymmetries do exist but can be appreciated only by “zooming-in” (here’s the intuition behind the idea). This counterintuitive insight was actually Coase’s own frustration with policymakers -we cannot assume full efficiency because transaction costs are really never zero. To elaborate on the point, we can consider the dynamics of a “phase change”, which can be explained using also complexity science and statistical physics but hold beautifully in social systems. From this perspective, we are zooming-in into a latent state.

A practical example using empirical data

The graph below maps the attention flows from services used by the bitcoin cash and bitcoin communities in the period from 1 month before the hard fork to 1 month after the hard fork. The network clearly shows how audiences interests are sufficiently different to likely support both currencies. The shared space includes common interests (such as wallets that supported both coins). The strength of the links encodes proximity, a measure of affinity between each service and the community — each particular cryptocurrency is a sink, a consumer of attention of the users of a service.

Figure 1. BCH & BTC ecosystems

The nodes are vertices of attention, the small ones function as sources and the large ones as sinks. In this example the focus is on the “off-chain” economy, but the same treatment can be applied to on-chain signals.

Proximity is what is called in mathematics a “distance metric”. A number of parameters are considered, including estimated geographical origin and various demographic factors, volume, semantics, expressed interests, etc.

Therefore, all these relationships are quantifiable: even while BCH’s ecosystem is smaller, the maximum proximity of the sources of attention is 5.56%, larger than BCT’s 0.99% — fitness can make a new coin competitive even when facing a formidable incumbent. In the matrix below, which is a sample from the network, darker color means higher proximity. The sources are services and the targets the bitcoin cash and bitcoin economies.

Figure 2. Matrix form

Note how bitcoin has a more diverse economy -it generates attention output from more services- and how most services are no ubiquitous across networks-each economy tends to be specialized on a certain type of attention product/service, at least during a period of time. While some of the relationships might be trivial (e.g. current users of a forked version of BTC such as Bitcoin ABC should gravitate easily to a new fork), others may encode useful investment information, such as crypto geo-political “factors”: users of Australian exchanges were more inclined towards BCH, over the counter investors in Canada remained mostly focused on BCT, Russians divided their attention.

The macro view: Say’s Law

Say’s Law (also known as the Law of Markets) which has been considered the most fundamental law in classical economic theory, states that at the macro level, aggregate production inevitably creates an equal aggregate demand. Since a fork is really an event at the macroeconomic level (in this case, the economy of bitcoin cash vs the economy of bitcoin), the aggregate demand for output is determined by the aggregate supply of output — there is a supply of attention before there was demand for attention. This view is much in the spirit of the use of the Equation of Exchange (MV=PQ) in the valuation of crypto economies, where each protocol is analyzed like its own separate economy.

Attention is a fluid thing. While hoarding for capital formation is a well-known fact in crypto economies, in terms of attention flows there can never be oversupply because at some attention price point there always will be a consumer. That is, the technologies of the old and new coins are close enough to ensure that users do not have to over-invest time and energy to take advantage of the opportunity — holders may even have access to “free money” if their wallets support both coins. But at the same time, the stock of interests from each community is unbalanced and separated enough so that there are points of attraction, where attention can flow by gravity.

That flux may also help explain why some minor altcoins that serve communities in which common interest is shared, resist dying: as long as there is attention flowing, some sort of passive or active transactional activity takes place. This activity may appear to obey mainly profit-seeking behavior (such as the miners’ capacity rebalancing towards a dominant chain right after a hard fork), but this is also just an expression of where the stream of attention first flowed.

Figure 3 shows attention inflows from one thousand services to the economies of bitcoin, bitcoincash, bitcoinxt, bitcoinunlimited and bitcoinclassic, and the flows in between those economies. The detail in Figure 4 shows a sample with the streams towards bitcoin classic: the main contributor (21.44%), is a market data service of systemic importance (contributes 44.93% and 51.74% to the attention economy of the two largest coins, BTC and BCH, and 3.33% to another of the smaller forks).

Figure 3. Full network, bitcoin forks
Figure 4. Bitcoin classic detail

The links in Figure 3 are pair-wise relationships (when a flow of attention exist) and the streams in the Sankey diagram are the share of attention, in this case using ISP and web panel data.

Attention is a valid proxy for economic activity when choosing signals with predictive power — strong variable sensitivity, in machine learning speak. As a matter of fact, besides the “on-chain” economy that usually makes the headlines, there is an “off-chain” crypto economy where economic formation happens when groups explicitly commit resources. Think for instance of the thousands of professional traders that pay hundreds of dollars each quarter for access to private chats where they discuss calls on entry/exit points. Attention pricing in those trading signals services can be quantified and it has a direct impact on the larger “on-chain” transactional economy.

And there are many examples of such micro-economies.

Economic complexity

The Economic Complexity Index (ECI) introduced by Cesar Hidalgo (MIT) and Ricardo Hausmann (Harvard) provides the ability to predict future economic growth by looking at the production characteristics of the economy as a whole, rather than as the sum of its parts.

Formally, the mathematical definitions are as follows,

Figure 5. Measuring Economic Complexity. Source: Atlas of Economic Complexity

And the relationships (the product space of a country) can be visualized either in matrix form or as a network graph,

Figure 6. Product space of a country’s economy. Source: Atlas of Economic Complexity

Note how the proximity between productive clusters encodes production capability: low tech industries are far apart from high tech industries, similar products within an industry share the same color and are clustered together, and enablers are closer (i.e machinery and chemicals should be present to allow for an electronics manufacturing industry to flourish).

In Figure 1 the nodes (online communities, commercial services, etc) are definitely connected between each other, but since the objective of the visualization is to highlight the overlap between the economies, for simplicity intra-node links are not shown. For the same reason proximity there is depicted with link tone rather than length. Adding all links will bear a resemblance to Figure 6.

The key insight from Hidalgo’s and Hausmann’s work is that “the complexity of an (country) economy is related to the multiplicity of useful knowledge embedded in it, and that hard to transfer, tacit knowledge is what constrains the process of growth and development”. In other words, the present information content of the economy is a predictor of future growth. We have to make adaptions to apply this concept to crypto economies, but since international trade flows and information flows are abstractions with universal properties, the key principles hold surprisingly well.

Enter Crypto Economy Complexity

While economic complexity is measured by the mix of products that countries are able to make, crypto economy complexity depends on the remixing of activities. In this sense, specialization is a kind of division of labor — do investors become simultaneously experts in ICO valuation, crypto hedge funds operations, crypto contracts for difference betting, smart contract programming, and so on, or do they seek for social validation from the experts on each of these fields? If you look again at the network of bitcoin forks this is the story that is telling us: competitive coins not only are supported by hashing capacity and other characteristics that can be considered as economic fundamentals, but they rely on attention flows from a diverse pool of difficult-to-transfer knowledge. You should know who knows.

We can also distinguish between on-chain events, which are usually related to the operation of the protocol and tangible transactional activity, and off-chain events, which can be any relevant signal — for instance, hits from filtered web services or API calls. Instead of making products, these economies produce sources of attention (from/to a service). And this productive knowledge is embedded in the governance and market structures of the society — this is why a great many of the services that drive economic activity in crypto economies are essentially “social fabric”, such as forums, engaging news bots, and over-the-counter exchange brokers. You should know where the required knowledge of those interacting agents (either people or machine) is aggregated.

A revealed comparative advantage is present when the economy captures attention above its fair share — as we saw in the case of BCH, in the matrix view of Figure 2. Think about that for a minute. Traffic revealed stronger knowledge intensity in BTC mining software (as you would expect from a more mature currency), but interest in BCH mining pools was of a similar quality (same color tone, similar proximity) as BTC’s. Poor attention in such a critical part of the economy should doom a forked coin — we are not talking vanity indicators (in this context, think social network “likes”), but an actual economic activity-enabling knowledge. Only if the agents in the economy get smarter, the competing blockchain or token can prosper.

That’s in principle the information content of the crypto economy. But the definition of an economic agent not only applies to human activities: automated interactions, such as demand signals generated by bots operating in exchanges, reveal the preferences of their optimization-seeking users. And it only makes sense for a crypto economy to develop strength in services that are affine: this is why a clear path of attention is drawn from BCH wallets to the BCH economy, and not to BTC’s (i.e. it will make little sense for users not interested in claiming BCH to try to accumulate knowledge about BCH wallets).

Time evolution of the network

Increased economic complexity is necessary for a society to be able to hold and use a larger amount of productive knowledge -Hausmann, Hidalgo et al.

It is important to understand the dynamics of crypto networks’ productive structures for two reasons: structure changes over time, and, knowledge dies if it is not transmitted. It is possible to simulate those changes because the social structures behind crypto communities follow well-known models. Let’s analyze the particular case of the social network producing attention towards the Bitcoin SegWit2X hard fork.

We looked at a sample of 4 431 social media mentions that covered the topic of B2X (the new forked coin) in the period of October 17–24, 2017. Most of those came from users on Twitter, Reddit, and Bitcointalk, and discussed topics such as mining of the new coin and futures contracts. The user that generated the most volume was actually a bot, which generated 4% of the volume and had 65 followers. Now, let’s assume that those followers are mostly human and reasonably well connected, as it will be expected in small tribes such as crypto communities. We can use the Watts–Strogatz model to generate a random graph with “small world” properties, such as a social network,

Figure 8. Clustering, sample from the Bitcoin B2X social network

What the resulting graph depicts is the information diffusion using density heat maps to analyze connectivity and nearness. A highly clustered version of this social network (red) is more robust and will allow the information to spread similarly. In other words, as members of the community specialize in different aspects of the economy, the structure of the network itself becomes an expression of the composition of attention output.

The example pertains mainly to the progression of social structure formation, how it is a fact of nature that participants tend to cluster together and that this kind of division of labor is a necessary condition for economies to prosper. To map the conversation dynamics we would need to create a series of directed graphs (i.e. adding arrows between nodes) and from there we could solve the minimum-cost flow problem (find the cheapest possible way/the best delivery route for sending a certain amount of flow across the network); we would then find that since each cluster is a specialized group, you do not need to broadcast all information to everybody all the time -a significant gain in efficiency.

We can also superpose multiple layers (what is called a multiplex network) to obtain an approximate portrait of the expected evolution of knowledge-containing structures within a crypto economy. And, by comparing those meta-structures across economies it is possible to project the strength of the social cohesion — that in turns is transformed into economic activity.

Now, there is another interesting phenomenon that is quite common in crypto. Often agents with perverse intentions (e.g. ICO scammers) compete for attention and disseminate information/misinformation in order to exploit trust. This also takes advantage of the information diffusion characteristics of networks, and can be analyzed using epidemic diffusion models — as one can imagine, the recovery rate of a node will be low because trust is not only scarce but fragile.

Rankings

Ultimately, quantifying economic complexity is about ranking economies. The problem here is that the ECI approach attempts to find the answer recursively based on a set of well defined products that are more or less unchanged, while in a crypto economy the sources of attention change constantly due to the swift pace of innovation — so there is no standardized classification of products as in international trade, and the result will never converge. Also, in the case of countries the relationships are binary (either a country produces a product or not = a link exists in the network or not), while in a crypto economy the strength of the attention signal matters — this is why the boxes in the matrix on Figure 2 are colored with different intensities.

Now, if we borrow a metaphor from mainstream finance, where the flow is the net of all cash inflows and outflows in and out of various financial assets, an alternative comes into view. Figure 9 shows the progression over three months on the intensity of the outflows emerging from the bitcoin cash economy, where size is the share from each service, and color intensity encodes the comparative scale of each service, and the most recent period is stacked at the bottom. The treemap depicts usage of various services that support the BCH economy, and the intra-economy flows between BCH and other coins.

Figure 9. BCH attention outflows, July to September 2017

As we can see, this is a dynamic system: the sources from the BCH economy evolve from informational services (e.g blogs) to economic activity enablers (such as payment apps, supporting exchanges, and so on) and new services (e.g different types of wallets), that become more or less relevant as competition for attention increases.

If the net of inflows and outflows encode the complexity of the economy, in essence, we are talking about an information theoretical problem. We could, for instance, use a Hidden Markov model to infer a unobserved sequence of events from the observed outputs (outflows). The Markov method is formally considered memory-less (i.e. only the present state matters), but in practice, it can be implemented with the memory of a number of previous events.

Modeling aside, there exist a sort of “value by memory” that can be derived from empirical data. Being the larger crypto economy essentially a closed system (there are still limits to the rate on the absorption of knowledge, so in small windows of time, churn in one community more or less equals gains in others), memory decay and re-wiring of links are quite common.

Another interesting observation is that it is very difficult to sustain attention after an extraordinary event -for instance, there was a spike in services interest and usage across the board during the crypto rally back in June 2017, but despite overall growing business, no one has seen those exact same levels of activity since then.

Now, let’s consider other possible approaches to ranking the crypto economies.

Valuation and ICOs: Trust is what matters

Let’s suppose that we need to rank two economies that appear close to identical in terms of knowledge intensity (e.g tokens with very similar use case and public visibility). For such a pair of crypto economies: if a service is not ubiquitous, that will signal higher specialization in one of them; if the economy is more diverse, that is a sign of strength.

As a case in point, we look at Augur and Gnosis, the prediction markets. Let’s begin by plotting returns, defined as the current dollar value of a $1 investment at the time of token sale. We identify peaks at 59.27x (Augur) and 12.16x (Gnosis), so from an investment perspective, both tokens show different performance. But what are the sources of such dissimilarity?

Figure 10. Peak returns. Source: TokenData

Figure 11 plots the ranges of contribution from the largest sources of attention to the economies of both tokens (Augur on top), during the same period.

First, we note the binary nature in the share of sources: often one token captures all of the attention of an important service, in detriment of the other which gets nothing.

Or there is a combination of smaller contributing services, as in the case of 100% of attention from a popular newsletter that went to the economy of one token.

Shared sources tend to be the usual suspects: news outlets, ICO trackers, and the like.

Figure 11. Top 22 attention sources

But there are also moments when a lagger can show increased strength. For instance, in July, Stox (another prediction market that just held an ICO on August) captured a larger share of attention than its peers: monopolized Facebook (97.52%) and Twitter (54.67%), Bitcointalk (83.95%), Steemit (64%) and VKontakte (83.93%).

Even when considering a crude proxy for attention, such as web activity, there was a temporary monopoly in terms of direct visits (47.9%). However, in September after the ICO had concluded, the attention finally converged to the same level of Augur and Gnosis. And again, we see how there’s clearly a dominant attention economy.

Figure 12. Prediction markets normalized attention inflows, Jul-Sept 2017

This “bursting” pattern in the signal hints at the possibility of applying methods inspired by biology. For instance, we can use genetic programming to find drivers — in other words, learn the rankings.

Such a ranking score function has the form,

returns_tokenA > returns_tokenB = f (sources_tokenA > sources_tokenB)

Where each source is weighted according to the total contribution to the group of tokens.

The scoring function may also include delayed effects, to reflect on the time-dependent nature of the relationship between financial returns and attention flows (i.e. current performance as a function of previous visibility & demand).

The Spearman’s Rank Correlation should be the error measure of choice for the machine learning model, since it is agnostic to the exact values and simply measures the correlation of putting tokens in the same order -the only assumption is the ability to sort the objects (crypto economies) according to each given attribute (sources of attention).

Trust is built when visibility increases, and, trust is resolved when investment is realized.

There is no one-size-fits-all attention metric because you need to be context-aware and optimize for different objectives and risk appetites. What matters here is that attention is one of the key elements of a trust decision system, being the others the probability of gain, the expected gain, and the fraction of capital that you are willing to risk.

Wrapping up

In essence, both Say’s and the ECI approach are about aggregation of dispersed resources, and that’s what makes those so relevant to the study of decentralized systems.

Some services are complex because few crypto economies consume them, and the crypto economies that consume those tend to be more diversified.

We should differentiate between the structure of output (off chain events) vs aggregated output (on chain, strictly transactional events). Until now most valuation proposals have focused on the second, leaving the first in the realm of non-scientific due diligence — applying various degrees of rigorosity, but still leaving open too many questions.

But it can be demonstrated that crypto economies tend to converge to the level of economic output that can be supported by the know-how that is embedded in their economy — and is manifested by attention flows. Therefore, it is likely that a crypto economy complexity is a driver of prosperity when complexity is greater than what we would expect, at a given level of investment return.

What are the practical implications?

It may sound odd, but the transition to a trustless financial system is all but frictionless.

Going back to predictive power: you can estimate the probability of certain events occurring on a certain timeframe based on known constraints of the system because although attention can switch instantly, there are physical limitations in the capacity of the current system and its connection to the mainstream financial system.

Think about offramps from exchanges. Let’s say that close to a fork it becomes evident that something really wrong will happen. Even a three days lead time won’t be enough to run to safety because most wire transfers will take longer than that. Now, there are private banking services that hold the equivalent to Nostro-and-Vostro accounts with exchanges to facilitate the operation of arbitrage traders and should benefit from this (and that can be measured using the flows approach). But even those fiat banking platforms have limitations in the amount of business they can handle when a catastrophic, fat tail event occurs. And if some are located in jurisdictions that happen to have banking holidays days before the fork, that stresses the system even more.

Would something like that be a definitive blow to the nascent “crypto organism”? Perhaps not, but without having a comprehensive understanding of the relevant parts of the system and how they interact it is impossible to meaningfully forecast emerging behavior. This type of knowledge exists, but as attention, it is scarce.

Ultimately, the degree of complexity is an issue of trust or lack thereof, and that’s what the flow of attention and its conversion into transactional events reveal.