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\begin{document}

\title{Crypto Economy Complexity}

\author{Dr. Percy Venegas\\ Economy Monitor }


\maketitle

\selectlanguage{english}
\begin{abstract}
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 token space will be
a destructive force or not. 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 use Coase's theorem. For the theorem
to hold, the conditions that the crypto communities that will split
should meet are: (i)Well defined property rights: the crypto investor
owns his attention; (ii) 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 digital asset) will come later; (iii) 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 assets) are mainly
speculative. The condition of symmetry refers to the ``common
knowledge'' available at t-1 where all that people know is the existing
asset. Information asymmetries do exist at the micro level -we cannot
assume full efficiency because transaction costs are really never zero.
Say's Law 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. The Economic Complexity
Index (ECI) introduced by Hidalgo and Hausmann allows to predicting
future economic growth by looking at the production characteristics of
the economy as a whole, rather than as the sum of its parts i.e. the
present information content of the economy is a predictor of future
growth. Say's Law and the ECI approach are about aggregation of
dispersed resources, and that's what makes those relevant to the study
of decentralized systems. 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. 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). 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. 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. We use
genetic programming to find drivers --- in other words, to learn the
rankings. Such a ranking score function has the form, returns\_tokenA
\textgreater{} returns\_tokenB = f (sources\_tokenA \textgreater{}
sources\_tokenB). Ultimately, the degree of complexity is an issue of
trust or lack thereof, and that is what the flow of attention and its
conversion into transactional events reveal.%
\end{abstract}%



\textbf{Keywords:}~blockchain, cryptocurrencies, ICO, behavioral
finance, complexity economics, complex networks, trading signals, market
microstructure, market design, trust economics, fields finance.

\par\null

\textbf{JEL Classification:}~G02, L14, E03,~D85,~C53

\par\null

\begin{quote}
``men err in their productions, there is no deficiency of demand''
-David Ricardo
\end{quote}

\section*{Introduction}

{\label{676966}}

All parties involved in an ICO (Initial Coin Offering) 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
usually favor to get rich quickly and then move to a different venture.
Sometimes the real motivation for large investors to 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 have more confidence if
they can trust that the founding team has a roadmap to value that is
validated by the market.

\par\null

Algorithm traders of coins and tokens 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. But
crypto economies are a novel phenomena --- there is little clarity on
how competition really works and when value is at risk. In the words of
an industry observer: 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?~\cite{sokolin}

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 helps explain differences in the
level of income of whole economies, and more importantly, 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.

\section*{Literature}

{\label{150984}}

\subsection*{The micro view:
Coase's~Theorem}

{\label{682748}}

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
trust-less 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'' \cite{Coase}. For the theorem to hold, the
conditions that the crypto communities that will split should meet are:

\emph{Well defined property rights}: the crypto investor owns his
attention.

\emph{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 or token) will come later.

\emph{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 digital assets) are
mainly speculative.

The condition of symmetry refers to the common knowledge available
at~\emph{t-1~}where all that people know is the existing digital asset.
Information asymmetries do exist but can be appreciated only by
``zooming-in''-- as one would do by applying gradient descent to take
ever smaller steps to reach a goal. 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 in social systems, as Harmon et al.
demonstrated in the work on prediction of collective panic in stock
markets \cite{Harmon_2011}. From this perspective, we would be
zooming-in into a latent state.

\par\null

\subsection*{The macro view: Say's~Law}

{\label{675233}}

Say's Law (also known as the Law of Markets) which has been considered
the most fundamental law in classical economic
theory~\cite{Jonsson_1999}, 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 (for instance, 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~\emph{before}~there was demand for attention.

\par\null

This view is much in the spirit of the use of~the Equation of Exchange
(\emph{MV=PQ}) that is commonly applied in the valuation of crypto
economies, where each protocol is analyzed as its own separate economy
--only that in this case, is not the monetary base and velocity of money
which is balanced-out with quantity of crypto and the price of a basket
of digital goods, but rather attention flows. When a fork occurs, or a
token is issued targeting the same audience and use case, there is a
competition for attention that has to be resolved at the macro level
because the larger crypto economy cannot produce enough informed
investors rapidly enough.~ ~

\par\null

\subsection*{Economic complexity}

{\label{717075}}

The Economic Complexity Index (ECI) introduced by Cesar Hidalgo (MIT
Media Lab) 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 \cite{Hidalgo_2009}.

\par\null

Formally, the mathematical definitions are as shown in Figure 1.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/ECI-definitions/ECI-definitions}
\caption{{Formulation of of the network model of ECI
{\label{614079}}%
}}
\end{center}
\end{figure}

And the relationships (the product space of a country) can be visualized
either in a matrix form or as a network graph, as in Figure 2.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/product-space/product-space}
\caption{{Network visualization of the product space
{\label{696728}}%
}}
\end{center}
\end{figure}

\par\null

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). The key insight from Hidalgo's and Hausmann's work is that
``the complexity of a (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 well.

\par\null

\pagebreak

\section*{Methods and discussion}

{\label{289847}}

Data for this section includes digital assets historical monthly returns
(Coincheckup.com), on-chain metrics such as fees and transaction volume
(Coinmetrics.com), and off-chain web and social analytics
(EconomyMonitor.com). We refer to the digital asset of the bitcoin
network as ticker BTC, and that one of the bitcoincash blockchain as
BCH.

\par\null

\subsection*{Micro case}

{\label{448263}}

\subsubsection*{Application of Coase's~Theorem using empirical
data}

{\label{185632}}

The graph in Figure 3 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 (July to August 2017). The
network shows how audiences interests are sufficiently different,
which~likely offers an opportunity to support both currencies. The
shared space includes common interests (such as wallets that supported
both coins). The strength of the links encodes~\emph{proximity}, a
measure of affinity between each service and the community --- each
particular cryptocurrency network is a sink, a consumer of attention of
the users of a service.

\par\null\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/BCH-BCT/BCH-BCT}
\caption{{BCH \& BTC ecosystems, top 2000 services by traffic countribution
{\label{520377}}%
}}
\end{center}
\end{figure}

\par\null

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. We could also slice the network views into temporal states
(e.g. monthly, weekly or daily) to better appreciate the progression of
the relationships between the services and their associated
crypto-economy.

Proximity is a distance metric included in the original dataset from the
click-stream data provider. A number of parameters are considered,
including estimated geographical origin and various demographic factors,
traffic volume, semantics, and, expressed interests. 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\% ---~\emph{fitness}~can make a new coin
competitive even when facing a formidable incumbent. In the matrix of
Figure 4, 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.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.28\columnwidth]{figures/matrix/matrix}
\caption{{Matrix~form from a 24-services sample of the~BCH \& BTC ecosystem
{\label{739184}}%
}}
\end{center}
\end{figure}

\par\null

In Figure 3 the nodes (online communities, commercial services, etc) are
in practice 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 is depicted with link tone rather than length. Adding all
links will bear a resemblance to Figure 2.

Note how bitcoin has a more diverse economy (it generates attention
output from more services), and how most services are not 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.

\par\null\par\null

\subsection*{Macro case}

{\label{482924}}

\subsubsection*{The fluid nature of
attention}

{\label{871195}}

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~\emph{stock of interests~}from each community is unbalanced and
separated enough so that there are points of attraction, where attention
can flow~\emph{by gravity}.

\par\null

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.

\par\null

Figure 5 shows attention inflows from one thousand services to the
economies of bitcoin, bitcoincash, bitcoinxt, bitcoinunlimited and
bitcoinclassic, and the flows in between those economies. Inflows are
measured by incoming visits.~

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/adjmatrix/adjmatrix}
\caption{{Full network, bitcoin~forks
{\label{845299}}%
}}
\end{center}
\end{figure}

\par\null

The detail in Figure 6 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).

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bitcoinclassic-inflows/bitcoinclassic-inflows}
\caption{{Sankey diagram view, Bitcoin classic~detail
{\label{544970}}%
}}
\end{center}
\end{figure}

The links in Figure 5 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.

\par\null

Attention is a valid proxy for economic activity when choosing signals
with predictive power --- strong variable sensitivity, in machine
learning terms. 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. For instance, there are 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~\cite{venegas2018} in those trading signals services can be
quantified using a similar network-view approach, and it has a direct
impact on the larger ``on-chain'' transactional economy. And there are
multiple examples of such micro-economies.

\par\null

\subsection*{Crypto Economy Complexity}

{\label{512022}}

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,~\emph{specialization}~is a kind
of division of labor --- do investors become simultaneously experts in
ICO valuation, crypto hedge fund operations, cryptocurrency 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
before making a decision? If we inspect the network of bitcoin forks we
find that 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. One should know those~\emph{who}~know.

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, requests for 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~\emph{where}~the
required knowledge of those interacting agents (either people or
machine) is aggregated.

A r\emph{evealed 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 4. 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 --- this is not
about vanity indicators (in this context, metrics such as 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.

This is, 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).

\par\null

\subsubsection*{Time evolution of
the~network}

{\label{694759}}

According to Hausmann, Hidalgo et~al, increased economic complexity is
necessary for a society to be able to hold and use a larger amount of
productive knowledge~\cite{2014}.

\par\null

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 us 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.~Let us 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, as shown in Figure 7.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/clustering-social-graph/clustering-social-graph}
\caption{{Clustering, sample from the Bitcoin B2X social~network
{\label{172023}}%
}}
\end{center}
\end{figure}

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, there is no need to
broadcast all information to everybody all the time -- a significant
gain in efficiency.

We can also superpose multiple layers (i.e. create 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.

There is another interesting phenomenon that is quite common in crypto
economies. 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 ~ \cite{Lawyer_2015} ( as one can imagine, the
recovery rate of a node might be low because~trust is not only scarce
but fragile) , or using game theory-based models~\cite{Aymanns_2017}.

\par\null

\subsubsection*{Rankings}

{\label{340877}}

Ultimately, quantifying economic complexity is about ranking economies.
The problem 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 could not converge. Also, in the case of countries the
relationships are binary (either a country produces a product or not,
that is, 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 4 are colored with different intensities.

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 8 shows the progression
on the intensity of the outflows emerging from the bitcoin cash economy
over three months, 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.

\par\null\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/bch-outflows/bch-outflows}
\caption{{BCH attention outflows, July to September 2017
{\label{274216}}%
}}
\end{center}
\end{figure}

As we can see, this is a dynamic system: the sources~\emph{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 an unobserved
sequence of events from the observed outputs (outflows). Although the
Markov method is formally considered memory-less (i.e. only the present
state matters), in practice, it can be implemented with the memory of a
number of previous events.

Modeling aside, there exists a sort of ``value by memory'' that can be
derived from empirical data. Being the larger crypto economy essentially
a closed system (i.e. 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
of June 2017, but despite overall growing business, those exact same
levels of activity were not observed until November and December 2017.

\par\null

\textbf{Ranking tokens}. So far we have discussed comparative
measurements among coins, but we should consider other possible
approaches to ranking alternative crypto economies. Let us 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 us begin by plotting~\emph{returns} (Figure 9), 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?

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/returns/returns}
\caption{{Peak returns. Source: TokenData
{\label{558263}}%
}}
\end{center}
\end{figure}

Figure 10 plots the ranges of contribution from the largest sources of
attention~\emph{to}~the economies of both tokens (Augur on top), during
the same period. The box plot diagram shows relative traffic share to
the websites of both projects.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/shares-of-sources/shares-of-sources}
\caption{{Top 22 attention sources
{\label{280335}}%
}}
\end{center}
\end{figure}

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

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\%), Twitter (54.67\%), Bitcointalk
(83.95\%), Steemit (64\%) and VKontakte (83.93\%). Even when considering
a basic proxy for attention, such as web activity, there is 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. Figure 11 shows how there is clearly a dominant
attention economy (Augur's) despite the transient bursts of activity
from other smaller players.

\par\null\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/prediction-markets/prediction-markets}
\caption{{Prediction markets normalized attention inflows, Jul-Sept~2017
{\label{155896}}%
}}
\end{center}
\end{figure}

This ``bursting'' pattern in the signal hints at the possibility of
applying methods inspired by biology. For instance, we could use genetic
programming~\cite{Schmidt_2009} to find drivers --- in other words, learn
the rankings. Such a ranking score function has a form as in Equation 1,

\par\null

\(returns_{tokenA}>returns_{tokenB}=f(sources_{tokenA}>sources_{tokenB})\)

\par\null

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 is 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).\href{https://iaes.confex.com/iaes/83am/webprogram/Paper13257.html}{}

There is no one-size-fits-all attention metric because one needs to be
aware of the context and optimize for different objectives and risk
appetites. What matters 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 the investor is willing
to risk~\cite{J_sang_2004}. And that trust is built when visibility
increases, while trust is resolved when an investment is
realized~\cite{krabec2017}.

\subsubsection*{Rankings heuristics}

{\label{607732}}

The machine learning-genetic programming approach is applicable to both
tokens and coins. Let us demonstrate step by step how it is applied to
the BCT-BCH case.

\par\null

\textbf{Traffic share.}~We sample the top 1000 sources that are shared
by both bitcoin and bitcoincash over a period of 6 months, from August
2017 to January 2018. To make the sources of attention representative,
we select bitcoin.org and bitcoincash.org as the attention sinks.~Figure
12 shows how the distributions are different: bitcoin captures the
larger share of traffic from most sources (80\% or higher), while
bitcoincash has more sources that are small contributors (20\% or
lower).~

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/paired-histogram/paired-histogram}
\caption{{Paired histogram, traffic sources
{\label{988618}}%
}}
\end{center}
\end{figure}

\par\null

\textbf{Contribution.}~However, the ``market share'' of each attention
economy has to be modulated by the contribution of each source --- as we
saw before, some sources have a~disproportionately~large weight. Here we
look at the aggregate contribution from all sources towards both Bitcoin
and BitcoinCash, across 6 months. We see how the dominance of 3 sources
is clear, while there are hundreds of smaller contributors.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/log-histogram/log-histogram}
\caption{{Contribution. Log, LogCounts
{\label{353534}}%
}}
\end{center}
\end{figure}

\par\null

\textbf{Share over~time.}~To better understand the shape of the data we
construct an array, in which the vertical axis represents the passage of
time (from August at the top, to January at the bottom), the cells in
the horizontal from left to right are each one of the first 200 sources
(we take this smaller sample from the top contributors from the 1000
sources, for simplicity of analysis and visualization), and the colors
encode the traffic intensity (yellow is high, blue is low, red is no
data).

\par\null\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/fat-array-bitcoin/fat-array-bitcoin}
\caption{{bitcoin, array of variables~
{\label{111908}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/fat-array-bitcoincash/fat-array-bitcoincash}
\caption{{bitcoincash, array of variables
{\label{230583}}%
}}
\end{center}
\end{figure}

\par\null

We can verify that bitcoin has a virtual monopoly on attention (there is
very little red on its chart). There is also no apparent overlap in the
top sources for each crypto-economy --- this is a sign of
specialization. For instance, some forums clearly chose the bitcoincash
camp, and some statistics services adopted BCH as their niche specialty
(or became favorites of the bitcoincash community). Over there,
bitcoincash wins the contest for attention --- but since the
contribution of those sources to the overall bitcoin-bitcoincash economy
is small, their positive impact on the creation of value is not certain.

One thing that is striking to see is that time did not make things
better for bitcoincash: there is some creative destruction in the form
of services that bitcoincash came to dominate later, but there are not
really many. And few more that did not exist at the beginning came
online later as developers started building tools specifically for this
economy. But in general, the ones that were strong at the beginning
remained so across the whole period of time.

\par\null

\textbf{Predictive model.}~The first thing that we should note is that
these are fat arrays --- that is, they have too many variables and very
few observations. This is by itself a challenge for most machine
learning techniques unless an evolutionary algorithm is used.

\par\null

When we start learning ranking models, we interpret~\emph{returns}~as an
indication of value, and the demand signals from traffic sources (e.g.
average page visits) as the~\emph{drivers}~of that value. Since we are
constructing a ranking system, we are interested in the demand
relationships that optimize~\emph{BTC\_returns \textgreater{}
BCH\_returns}.

The first formula that we discover may appear as a trivial model: the
returns of BCH are larger when the influential site Bitcoin.com, an
advocate of BCH that also operates a wallet service, throws its weight
to support BCH. Model 1~ is shown (variable names are shortened for
readability).

\par\null

\((BTC_{returns})\ >\ (BCH_{returns})=(-BTCbitcoincom)\ >(-BCHbitcoincom)\)

\par\null

We keep running new generations of our evolutionary search (an
example,~see two more models in the Table of Figure 16), and more
informative relationships emerge; non-mainstream search engines where
demand signals begin to pop-up, also mining pools, and even
informational sites. Several iterations can be run, and if we do it over
larger sample sizes (instead of the 200 sources, we use the original
1000, or even 10.000) and more time periods (temporal steps measured in
weekly or daily returns, instead of months), likely many other
interesting relationships will appear.~

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/sensitivity/sensitivity}
\caption{{Model 3, 2, 1 variable sensitivity
{\label{714629}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/sensitivity-table/sensitivity-table}
\caption{{Variable sensitivity definition
{\label{875577}}%
}}
\end{center}
\end{figure}

This diversity points to an interesting fact: we should perhaps
deploy~\emph{model ensembles~\cite{Kotanchek}}, rather than standalone
models. And this makes sense: while in classical Economic Complexity
theory one deals with relatively unchanged basket of products that are
produced by the same countries, in a crypto economy new sources of
attention are born and die constantly, and the sinks of that attention
(the economies of each network) also are created at any time that a fork
occurs and a community rallies behind the new coin.

A final observation is that standalone models are fragile themselves --
they are either incomplete or lack sufficient explanatory power, as
shown in Figure 16-17. In that regard, our preferred anti-fragile
ranking system should be one that is flexible and robust --- as the
crypto-economies that are being analyzed themselves.

\par\null

\pagebreak

\par\null

\section*{Conclusions}

{\label{426802}}

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 (even when not using only blockchain
data, but rather off-chain data points).

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~\emph{structure of
output}~(off-chain events) vs~\emph{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's complexity is a driver
of prosperity when complexity is greater than what we would expect, at a
given level of investment return.

\par\null

\subsection*{Practical implications of this
research}

{\label{597966}}

It may appear strange, but the transition to a trust-less financial
system is all but frictionless.

In regards to predictive power, this research suggests that one can
estimate the probability of certain events occurring on a certain
timeframe based on known constraints of the blockchain financial 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.

For instance, one may think about off-ramps from exchanges. If getting
close to the date of a fork it becomes evident that the event will
create a major market disruption, even a three days lead time will not
be enough to run to safety because most wire transfers will take longer
than that. There are private banking services that hold the equivalent
to nostro-and-vostro accounts with exchanges to facilitate the operation
of arbitrage traders, and those should benefit from this situation (and
that can be measured using the flows approach). But even those fiat
banking platforms have limitations in the amount of business that they
can handle when a catastrophic, fat-tailed 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 such an scenario be a definitive strike to a 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.

Ultimately, the degree of complexity is an issue of~\emph{trust}~or lack
thereof, and that's what the flow of attention and its conversion into
transactional events reveal.

\selectlanguage{english}
\FloatBarrier
\bibliographystyle{apacite}
\bibliography{bibliography/converted_to_latex.bib%
}

\end{CJK}\end{document}

