The Network Effect

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THE DEBAUCHERY

OF CURRENCY

THE NETWORK EFFECT

TIMOTHY F. PETERSON, CFA, CAIA

Published by Freedom Fortune Press

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ABOUT THE AUTHOR With 30 years in institutional investment management, Timothy Peterson is a published author with expertise in alternative assets, including cryptocurrency investment and valuation.

Timothy authored the very popular “Metcalfe’s Law as a Model for Bitcoin’s Value,” which was the first peer-reviewed publication on how to value Bitcoin with Metcalfe’s Law. Based on downloads, his cryptocurrency research ranks in the top 0.05% of over 800,000 authors on SSRN. He has also written two books, “The Debauchery of Currency: A Bloody History of Money” and “Performance Measurement for Alternative Investments” (Risk Books: 2015). Timothy has spoken at conferences around the world on various investment topics.

He is a dual graduate of the University of Colorado with a Master of Science Degree in Finance and a Bachelor of Arts degree in Economics. He is a Chartered Financial Analyst and Chartered Alternative Investment Analyst and has also completed the Harvard JFK School of Government course on Investment Decisions and Behavioral Finance.

Timothy teaches “Digital Assets for Bankers” at the prestigious Graduate School of Banking at Louisiana State University.

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CHAPTER Y

THE NETWORK EFFECT “I'm sure that in 20 years there will either be very large transaction volume or no volume.”

—Satoshi Nakamoto, February 2010

W

hy do people join Facebook? The simple answer is the fact that many of your friends, family, and acquaintances are already there. This presence creates immediate value to you personally when you join, as it offers a convenient way to stay connected with the people in your life and to keep informed, and inform others, of the things that are personally important to you.

Why did your family join Facebook? Because many of their friends, family, and acquaintances are already there. And why did those people join? For the same reason. This is the network effect.

Facebook becomes more attractive as more users join. Each new user adds value to the platform by contributing content, sharing updates, and engaging in interactions. This growing pool of connections makes it easier to find and reconnect with people, whether they are from your past or present. The more people you know who are on Facebook, the more compelling it becomes for you to join and participate.

In essence, people join Facebook because it taps into the fundamental human necessity for connection and community. The network effect means that as more people join, the platform becomes more valuable to each user. This creates a self-reinforcing cycle of growth, where the increasing number of users continually enhances the experience for everyone involved. Facebook’s success is a testament to the power of the network effect in creating and maintaining a dominant social platform.

There is far more to the network effect than just following the crowd. Whereas Metcalfe’s Law describes the value of a network based iii

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on size, the network effect explains how and why networks form, grow, and behave the way they do. Metcalfe’s Law is quantitative. The network effect is qualitative. This chapter explores the nuances and conditions that create and perpetuate network effects: the good, the bad, and the ugly.

The network effect is more than just rapid growth. Not all networks, and not all digital applications, have or experience network effects. That is because network effects accrue to the users of the network, and not simply the administrators or owners of the network.

Imagine a network that starts with ten users. In this network, each user can connect with nine other users. The total number of unique connections is calculated using the formula 𝑉=

𝑛 × (𝑛 − 1) 2

where n is the number of users. For 10 users, the total number of unique connections is (10 × 9) / 2 = 45. This means each user can benefit from 45 potential transaction pairs spread across 10 users, making the value per user V/n = 45/10 = 4.5.

As the network grows to 100 users, the total number of unique connections becomes (100 × 99) / 2 = 4,950. This translates to a value per user of 4,950/100 = 49.5, significantly increasing the potential liquidity and transaction opportunities for each user on the platform.

When the network reaches 1,000 users, the total number of unique connections is (1,000 × 999) / 2 = 499,500. The value per user becomes 499,500/1,000 = 499.5. The network becomes incredibly valuable for each individual user because the sheer number of connection pairs offers extensive possibilities for increased and diverse interaction opportunities.

Doom, the iconic first-person shooter game developed by id Software and released in 1993, is a prime example of the network effect in action. This game not only revolutionized the gaming industry with its graphics and gameplay but also showcased how a network of users can significantly enhance the value of a product through peer-to-peer activity. Except for e-mail, it is widely regarded as the first computer application to “go viral.”

Doom was a critical and commercial success, earning a reputation as one of the best and most influential video games of all time. It 2

has been termed the “father” of first-person shooters and is regarded as one of the most important games in the genre.

One of the most significant innovations of Doom was its multiplayer mode. The game allowed players to connect over local area networks for cooperative or competitive gameplay. This feature was revolutionary at the time and laid the groundwork for modern multiplayer gaming. The multiplayer aspect of Doom exemplified the network effect, where the value of the game increased as more players joined. With each new player, the potential for exciting and varied multiplayer matches grew, making the game more attractive to additional players.

The company believed that the mainstream press was uninterested in the game and shunned advertising in gaming magazines. Instead, they gave software retailers the option to sell copies of the first Doom episode at any price, in hopes of motivating customers to buy the full game directly from id.

The development team at id uploaded the first episode to the internet, letting interested players distribute it for them. When the upload finished 30 minutes later, 10,000 people attempted to download the game at once, crashing the network. Within hours of Doom’s release, university networks began banning Doom multiplayer games, as a rush of players overwhelmed their systems.1 Doom became a literal overnight success, making a profit within a day after release. Although the company estimated that only 1% of shareware downloaders bought the full game, this was enough to generate initial daily revenue of $100,000. By May 1994, the game had sold over 65,000 copies, and estimated that the shareware version had been distributed over 1 million times. First year sales totaled over 150,000 copies at an estimated $1 million in revenue.

By late 1995, Doom was estimated to be installed on more computers worldwide than Microsoft’s new operating system, Windows 95.

By April 1998 Doom’s shareware edition had yielded 1.4 million units sold and $9 million in revenue in the United States. It is estimated that nearly 20 million people played Doom within 24 months of its launch.

The network effect of Doom has had a lasting impact on the gaming industry. Its success demonstrated the potential of multiplayer gaming and community-driven content creation. Many of the elements that made Doom a success are now standard in the industry, such as online multiplayer modes, modding support, and community

1 The author admits being affected by these bans, which forced gameplay into the middle

of the night when the servers were idle and the graveyard shift network administrator didn’t care.

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engagement. The game’s influence can be seen in countless subsequent titles that have embraced these concepts to build their own user networks.

The concept of the first mover advantage is widely recognized in the business world. However, it is often misunderstood. Critics point to examples such as the Palm Pilot, MySpace, and BlackBerry to argue that being the first to market does not guarantee lasting success. Interestingly, the fact that these brands are still well-known today underscores their initial success rather than their ultimate failure.

It’s essential to clarify that the first mover does not necessarily mean the literal first entrant into a market. Instead, it refers to the first incarnation to capture significant acceptance that consumers perceive as “good enough.”

Historical examples demonstrate that the actual advantage lies not in being the first invention or the first to market but being the first to achieve the critical mass necessary for widespread adoption. This nuance is crucial in understanding why certain “firsts” succeed and others do not. The Palm Pilot, for instance, was one of the first handheld personal digital assistants, yet it failed to maintain its lead. MySpace was a pioneer in social networking but was eventually eclipsed by Facebook.

BlackBerry revolutionized mobile communication with its email-centric smartphones but fell behind when the market shifted towards more versatile, consumer-friendly devices.

The success of a first mover hinges on its ability to offer something that meets the market’s needs effectively, even if it’s not perfect.

This is sometimes referred to as the “80% solution2”—a product that is “good enough” for a substantial number of users. The iPhone is a prime example of this principle in action. Before the iPhone, companies like BlackBerry focused on integrating computer technology into a phone.

These devices were excellent for email and business communications but lacked the broader appeal needed to capture the consumer market.

Apple’s genius lay in reversing the equation: people didn’t want a phone with a mediocre computer; they wanted a good computer that could also make phone calls. The iPhone combined the functionalities of a phone, a music player, and an internet browsing device into one sleek package. It wasn’t the first smartphone, but it was the first to deliver an

2 The term "80% solution" originates from the Pareto Principle, also known as the 80/20

rule. This principle was named after the Italian economist Vilfredo Pareto, who observed that roughly 80% of the effects come from 20% of the causes. In various contexts, it implies that achieving 80% of the desired outcome with 20% of the effort or resources is often sufficient and more efficient than striving for perfection, which would require disproportionately more effort.

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experience that resonated deeply with a wide audience. By providing a product that was “good enough” to meet the diverse needs of consumers, Apple secured its position as the dominant player in the smartphone market.

Understanding the true nature of the first mover advantage involves recognizing that early market entry alone is insufficient. There must also be a compelling value proposition that translates into utility for each user. Sometimes, even the market cannot articulate this value proposition. “If I had asked people what they wanted, they would have said faster horses,” is often attributed to Henry Ford on the success of the automobile. While the quote is unverified, the sentiment rings true.

The concept of the first mover advantage is particularly important to networks. Being the first significant network in a new space allows that network to capitalize on the network effect, leading to rapid growth before competing networks can establish themselves. This advantage is pivotal in creating the largest and most dominant network.

Network value creation is typically quadratic, meaning that the utility of the network grows proportionally to the square of the number of its users. As a result, early networks can grow rapidly and establish a significant market presence before competitors can catch up.

When a network is first to market, it has the unique opportunity to start growing before other networks can form. This early growth is crucial because it allows the network to achieve a critical mass of users, making it more attractive to new users. The first network to reach this critical mass becomes the largest by default, as it offers the most connections and interactions. In time, and as we will see later, this network will become indestructible. This was, in part, the reason Satoshi Nakamoto wrote “It might make sense just to get some in case it catches on. If enough people think the same way, that becomes a selffulfilling prophecy.”

Facebook is an excellent example of this phenomenon. Although it was not the first social network, it was the first to achieve widespread adoption by creating a platform that was “good enough” for a broad audience. One thing that made Facebook “good enough” to overtake MySpace would be the focus on real-life connections. Facebook encouraged users to connect with people they already knew in real life.

This emphasis on authenticity and real identities created a more trustworthy and engaging environment, setting Facebook apart from MySpace and driving its widespread adoption.

Once a network achieves a dominant position, it becomes increasingly difficult for new entrants to compete. The established network benefits from a large user base, which provides significant inertia. New networks must offer substantially superior value to persuade users to switch, which is a challenging proposition when the incumbent network already meets their needs effectively.

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The Microsoft Office productivity suite is an example of a network that established itself early in the software market. Now, most would not view MS Word, Excel, or PowerPoint as networks. However, their value lies in their interoperability with each other and with other users of that platform. The large number people initially using these software programs necessitated that others acquire them to read, modify, and redistribute the information that was created. This, in turn, required the addition of more users of Microsoft Office. Microsoft dominated productivity software for over 30 years.

The first mover advantage in networks is fundamentally about capturing the network effect early. Being the first significant network allows a company to grow quadratically, creating a dominant position before competitors can establish themselves. This early growth creates substantial barriers to entry, making it challenging for new networks to compete.

Bitcoin is often heralded as a revolutionary innovation in the world of digital money. However, it was not the first attempt at creating digital currency. Prior to Bitcoin, there were several initiatives aimed at developing electronic money systems, such as DigiCash, e-gold, and Liberty Reserve. These early systems introduced the concept of digital money but failed to gain widespread adoption due to various shortcomings. Bitcoin’s breakthrough lay in addressing several critical problems that its predecessors could not solve, with the preservation of purchasing power being the most significant.

Digital money has been a concept in the making for decades.

Early pioneers like David Chaum’s DigiCash in the 1980s and 1990s explored cryptographic solutions to enable private, untraceable transactions. Despite the technological advancements, these early digital currencies failed to gain traction due to centralization issues, regulatory challenges, and lack of trust from users.

E-gold, launched in 1996, was another attempt to create digital currency backed by physical gold. It provided an efficient way to conduct online transactions but faced severe legal and regulatory hurdles that ultimately led to its shutdown. Liberty Reserve, founded in 2006, also attempted to create a digital currency system but was shut down due to money laundering accusations.

These examples highlight that while the concept of digital money was not new, the existing solutions failed to address key issues such as security, decentralization, and long-term value retention.

Bitcoin’s most significant achievement was its ability to preserve purchasing power over time, addressing a fundamental problem that earlier digital currencies could not solve. For decades, people had been using 6

electronic money for transactions, but they were seeking a reliable way to store value digitally.

Before Bitcoin, digital money systems were largely focused on facilitating transactions rather than ensuring the preservation of value.

Traditional electronic money was tied to the fiat currency system, which is subject to inflation and devaluation. As a result, the purchasing power of electronic money could diminish over time, eroding savings.

Bitcoin’s design included several innovative features that collectively addressed these issues. The most crucial aspect was its distributed ledger, which eliminated the need for a central authority. This decentralization ensured that no single entity could manipulate the system or inflate the currency, thereby preserving its value over time.

The demand for a better way to save money was driven by the shortcomings of the traditional financial system. In many parts of the world, people faced high inflation rates, unstable currencies, and limited access to reliable banking services. These challenges made it difficult to save money and preserve wealth.

Bitcoin’s ability to preserve purchasing power has had a profound impact on the financial landscape. It has become a popular asset for individuals and institutions seeking to hedge against long-term inflation and economic instability. Its success has also spurred the development of numerous other cryptocurrencies, each aiming to build on Bitcoin’s foundational principles.

Moreover, Bitcoin’s success has led to increased interest in decentralized finance (DeFi) and blockchain technology, which are reshaping how financial services are delivered. These developments highlight the transformative potential of digital currencies in providing more inclusive and resilient financial systems.

Bitcoin was not the first digital currency, but it was the first to solve critical problems that plagued earlier attempts, particularly the preservation of purchasing power. By addressing the demand for a reliable savings mechanism, Bitcoin distinguished itself from its predecessors and established a new paradigm for digital money. Its innovations in decentralization, security, and transparency have set the stage for a new era in the financial world, demonstrating the importance of solving fundamental problems to achieve widespread adoption and success.

The most important thing a person can feel is to feel accepted. Acceptance fosters a sense of belonging, security, and selfworth, which are fundamental to mental and emotional well-being. It allows individuals to be authentic, express themselves freely, and build 7

meaningful connections with others. When people feel accepted, they are more likely to thrive, take risks, and pursue their goals with confidence.

This sense of acceptance can come from family, friends, community, or even oneself, and it plays a crucial role in shaping a person’s overall happiness and fulfillment in life.

So important is acceptance to the human psyche that excommunication, banishment, and exile have historically been among the harshest punishments reserved for society’s most egregious offenders.

The network effect applies to social and political groups. Individuals are incentivized to join and stay in groups because the benefits of being part of a larger, interconnected network often outweigh the costs of personal disagreement with some of the group’s tenets.

In political affiliations, individuals might align themselves with a particular political party not because they fully agree with its ideology but because being part of the party offers social and economic advantages.

These benefits can include access to social networks, job opportunities, and a sense of community and identity. The same is true for social movements and organizations; people may support causes or participate in activities that do not entirely align with their beliefs simply to gain acceptance and the perceived benefits of belonging.

This phenomenon can be seen in corporate environments as well. Employees may adopt the company culture and express support for corporate values, even if they privately disagree. The fear of being marginalized or missing out on career advancement opportunities often leads individuals to conform to the dominant norms and behaviors within the organization. The social capital gained from being part of the “in-group” can be a powerful motivator.

Moreover, social media platforms exemplify this dynamic. What foolish things will people say or do to generate an audience? Users often curate their online personas to fit into certain communities or to gain followers and likes. They may share opinions or content that they believe will be well-received, even if those do not reflect their true beliefs.

The network effect on social media creates an environment where conformity is rewarded with social validation, and dissent can lead to isolation.

From a network economics perspective, the desire for acceptance and the benefits of being part of a larger network drive individuals to conform to group norms. This can result in irrational behavior, where the fear of exclusion or the lure of social capital outweighs personal beliefs and values. Understanding this dynamic is crucial for fostering inclusive and supportive environments that allow for genuine diversity of thought and individual expression.

At some point, a group, technology, or belief reaches a level of critical mass that can be defined as acceptance. Metcalfe’s Law suggests that this level may be as few as 100 users.

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Of all the properties of money (portable, divisible, durable, scarce, and accepted), acceptance is the most important. Without acceptance, money fails to serve any of its primary functions: a unit of account, a store of value, and a medium of exchange.

In financial markets, acceptance translates directly into liquidity.

Liquidity refers to how quickly and easily an asset can be bought or sold in the market without affecting its price. An asset with high liquidity can be swiftly converted into cash or exchanged for some other thing with minimal loss of value, while a less liquid asset may require more time and potentially a price concession to sell.

Liquidity adds significant value to financial markets. Liquidity is perhaps the least appreciated source of value. Without it, there would be no transacting; and without the ability to transact, there is no market and no way to realize an asset’s value.

For money to function effectively as a medium of exchange, it must be widely accepted in transactions for goods and services. This acceptance creates a seamless flow of commerce, allowing individuals and businesses to trade efficiently. If money is not accepted, its utility collapses, and barter or other less efficient systems would have to be used instead.

Money’s role as a store of value depends on the confidence that it will be accepted in the future. This trust allows individuals to save and defer consumption, knowing their money will retain its purchasing power over time. If people believe that the money will not be accepted later, they will be less likely to hold onto it, undermining its value as a store of wealth.

Money provides a common measure for valuing goods and services. This standardization simplifies transactions and economic planning. In a sense, unit of account forces acceptance because the value of goods and services is measured in it.

In the mid-16th century, the Holy Roman Empire was a patchwork of semi-autonomous states, each with its own coinage. This lack of uniformity posed significant challenges for trade and economic stability.

The myriad local currencies varied widely in weight, metal content, and value, creating confusion and inefficiency in commerce.

The thaler, the precursor to the dollar, became the unit of account for the Holy Roman Empire with the establishment of the Imperial Mint Ordinance of 1566. This ordinance, issued by Emperor Maximilian II, standardized the currency system within the empire, making the silver thaler (or taler) the principal coin. The move was part of broader efforts to stabilize and unify the diverse monetary systems in use across the various states of the empire.

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The standardization of the thaler facilitated its acceptance across the empire by simplifying trade and providing increased liquidity. The uniformity of the thaler reduced transaction costs and minimized the risks associated with currency debasement and fraud. Not coincidentally, the unification of many currency networks into a single network maximized value, as we will see later.

Bitcoin gained acceptance through a combination of innovation and resilience. Despite facing plenty of bad publicity, Bitcoin’s history exemplifies the adage that There Is No Such Thing As Bad Publicity.

Each headline, whether positive or negative, prompted someone to ask, “What is Bitcoin?” This curiosity often led individuals to conduct their own research and educate themselves.

Bitcoin has faced numerous challenges, including regulatory scrutiny, market volatility, widespread skepticism, and outright derision.

Despite these hurdles, Bitcoin has demonstrated remarkable resilience.

This resilience bolstered confidence in Bitcoin’s long-term viability, even among early skeptics.

Just as acceptance is a psychological phenomenon that promotes value, persistence is a psychological phenomenon that promotes acceptance.

The Lindy Effect posits that the longevity of non-perishable items–such as ideas, technologies, or cultural phenomena–predicts their future lifespan. Essentially, the longer something has existed, the longer it is likely to continue existing. Named after a famous New York deli, Lindy’s, where it was noted that the longer a Broadway show ran, the longer it was expected to keep running, this effect has intriguing implications.

The Lindy Effect also intersects with the concept of anti-fragility—the idea that some things gain from disorder. Items that have withstood the test of time have typically faced numerous challenges and survived, showcasing their robustness. In investment, this means older, well-established companies or technologies might be safer bets than newer ones. For personal development, skills like critical thinking or communication, valuable for centuries, are likely to remain important.

For Bitcoin, the distributed architecture and incentive mining program–combined with network effects–translates into durability, the critical component to the store of value property of money. This durability creates longevity, which in turn is perceived as a Lindy Effect.

Through a process of education and engagement, many individuals moved from doubt to acknowledgement to understanding to acceptance.

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A Schelling point, named after the American economist and game theorist Thomas Schelling, refers to a solution that people tend to choose by default in the absence of communication because it seems natural, special, or relevant to them. Schelling introduced this concept in his 1960 book The Strategy of Conflict as a means of understanding how individuals coordinate their actions in strategic situations without the ability to communicate. Schelling points are pivotal in game theory, a field that examines how people make decisions in competitive contexts.

A classic example of a Schelling point is the scenario in which two people are asked to meet in New York City without specifying a time or location. Despite the countless possibilities, many people instinctively choose Grand Central Terminal at noon. This location and time serve as a Schelling point because they are prominent and central, making them natural focal points for coordination.

Schelling points can emerge in various contexts, from simple everyday decisions to complex international negotiations. They are particularly significant in situations where individuals must align their actions without direct communication. For example, consider the challenge of finding a parking space in a crowded lot. Drivers often adhere to an unspoken rule of taking the first available spot they encounter. This “lazy user” approach is ingrained in the way humans operate and is perhaps one reason Zipf3 named his book Human Behavior and the Principle of Least Effort.

Acceptance of a widely used product or service becomes a Schelling point due to network effects. When a significant number of people adopt a particular technology, platform, or standard, it becomes the default choice for new users. This is because the value derived from joining an established network often outweighs the benefits of exploring alternatives.

New users, including lazy users, are more likely to join Facebook over a new platform because their friends and family are already there, making it easier to connect and interact. A prospective user need not deliberate or compare multiple options; the obvious choice is the one that everyone else is using. This reduces the cognitive load and effort

3 George Kingsley Zipf (1902-1950) was an American linguist and philologist who stud-

ied the statistical distribution of word frequencies in natural languages. Zipf's Law, one of his most famous contributions, states that in any given corpus of natural language, the frequency of any word is inversely proportional to its rank in the frequency table. For example, the most frequent word will appear approximately twice as often as the second most frequent word, three times as often as the third most frequent word, and so on.

This phenomenon highlights a remarkable regularity in the patterns of human language and has implications for various fields, including linguistics, information theory, and social sciences.

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required to make a decision, aligning perfectly with the lazy user’s preference for simplicity and convenience.

This dynamic can also be observed in software ecosystems. Consider the aforementioned dominance of Microsoft Office in the realm of productivity software. Despite the availability of free alternatives like Google Docs or LibreOffice, many users stick with Microsoft Office because it is the standard in professional environments. The network effect here ensures that documents created and shared in Microsoft Office formats are universally accessible and compatible. For the lazy user, adopting Microsoft Office is a Schelling point because it minimizes the risk of compatibility issues and the effort needed to learn new software.

Bitcoin stands as a prime example of a coordination game within the cryptocurrency space, demonstrating how game theory principles can shape the evolution and adoption of digital assets. At its core, Bitcoin’s success relies on the collective recognition that adopting it as a common medium of exchange and store of value leads to a network effect benefiting all participants.

This widespread acceptance has established Bitcoin as a Schelling point in the cryptocurrency ecosystem. A Schelling point, or focal point, is a solution that people tend to choose by default in the absence of communication. For individuals entering the cryptocurrency world, Bitcoin often emerges as the natural choice due to its prominence and established network.

During the Ukraine invasion in 2022, Bitcoin played a crucial role in quickly funneling funds into the conflict zone. With cities and infrastructure under attack, traditional banking and money transfer systems broke down. In the early days of the war, people were desperate to send money to relatives. Others wanted to contribute directly to the defense effort.

Bitcoin was the obvious choice because people knew that it could be used for cross-border payments, without risk of being delayed, stopped, or confiscated by an intermediary. At the time, there were over 20,000 cryptocurrency alternatives that could have been used, along with the dominant fiat options. The fact that people overwhelmingly chose Bitcoin can be attributed to Schelling point theory.

A feedback loop is a system where the output of a process is fed back into the system as input, which in turn affects subsequent outputs.

This looping effect can either stabilize or destabilize the system, depending on the nature of the feedback.

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As more people use a network, its value increases for each user.

This added value attracts even more users, creating a self-reinforcing cycle.

A social media platform’s value to users increases as more people join it. This is because each additional user can connect with an increasing number of people, enhancing their experience and the utility they derive from the platform.

The cycle works as follows: the larger the network, the greater the value to each user; the greater the value to each user, the more new users are attracted; and the more new users are attracted, the larger the network becomes. This positive feedback loop continues to grow the network’s user base and value, often making the largest network the fastest growing, most valuable, generating entrenched dominance that is difficult–if not impossible–to unseat.

Bitcoin’s adoption illustrates a feedback loop driven by Metcalfe’s Law, which states that the value of a network is proportional to the square of the number of its users. In Bitcoin’s case, as more people start using and investing in Bitcoin, the network grows. This growth increases the network’s utility because the larger user base improves liquidity, acceptance, and trust. As Bitcoin becomes more valuable and useful, it attracts additional users and investors, further expanding the network and enhancing its value. This cycle perpetuates Bitcoin’s adoption until the ecosystem is satiated.

Lazy user behavior amplifies this loop. People generally prefer to use and invest in widely accepted and trusted assets, not to mention investments that go up. As Bitcoin’s network grows and its adoption becomes more mainstream, its price increases and individuals and institutions see it as a more reliable asset. This perception fuels further adoption, leading to a self-reinforcing cycle of growth and increasing value.

Feedback loops, acceptance, and adoption have their limits. An example of one such limit is Dunbar’s Number.

Dunbar’s Number is a proposed cognitive limit to the number of stable connections that an individual can maintain. Proposed by British anthropologist Robin Dunbar, the number is commonly cited as 150, although Dunbar himself suggested a range between 100 and 250. This concept has significant implications for understanding social structures, both in human societies and in the context of organizational and digital networks.

The origin of Dunbar’s Number lies in studies of primate brain sizes and social group sizes. Dunbar observed that there was a correlation 13

between the size of the neocortex–the part of the brain responsible for higher-order cognitive functions–and the average social group size of a species. Extrapolating this relationship to humans, Dunbar proposed that the human brain, specifically the neocortex, limits the number of meaningful social relationships an individual can maintain to approximately 150.

This limit reflects the cognitive constraints of the human brain in managing social information, including keeping track of relationships, social dynamics, and individuals’ histories and behaviors within the group. Beyond this threshold, the ability to maintain coherent and stable relationships deteriorates, leading to less cohesive and stable groups.

For example, in the US Army (and many others) the standard combat unit is the Company. A company typically consists of 3 platoons, and each platoon has four squads. Each squad has ten soldiers. Therefore, a company has 120 soldiers, with perhaps a few specialists for administration and inter-company coordination, etc. Maintaining units within a size that allows for strong interpersonal relationships enhances operational effectiveness. By aligning military unit sizes with the cognitive limits of human social capacity, military organizations optimize the social dynamics that are crucial for success in both peacetime and combat operations.

In the Roman Republic, the Comitia Centuriata was an assembly where century referred to a voting unit of individuals. The actual size of a century varied based on the wealth and military class of its members.

Initially, each century was intended to represent approximately 100 men, aligning with the literal meaning of the word century. However, over time, the sizes of centuries diverged from this ideal.

The Centuriata voted as groups rather than individuals, in other words, each century voted as a single entity. Members of each century would discuss and decide among themselves how to cast their single collective vote. There was no individual voting within the centuries; the decision was made by the century as a whole.

The organization of the Comitia Centuriata into centuries can be seen as an early acknowledgment of the principles underlying Dunbar’s Number. It allowed the Roman Republic to balance the need for broad citizen participation with the practical limitations of human social and cognitive capabilities. By keeping each century within a manageable size, the Romans optimized their political processes for the effective functioning of their society, demonstrating an intuitive understanding of the importance of group size in human social organization.

In modern contexts, Dunbar’s Number is also relevant to digital social networks. Platforms like Facebook and X allow users to connect with thousands of people, but studies suggest that users still primarily interact with a much smaller core group of contacts. This aligns with Dunbar’s hypothesis, indicating that while technology expands the 14

potential for connections, the cognitive limit on meaningful relationships remains.

When researching connectivity to test Metcalfe’s Law, Dr. Metcalfe found evidence of Dunbar’s Number in Facebook. Said Metcalfe, “[T]hat then raises the question, how many friends can you have? It turns out, there’s a sociologist who studied this for decades, Professor Dunbar and after many years, he discovered that the human brain has a capacity, cognitive capacity to have about 150 friends. There’s a little variability, but around 150. So, I called up Facebook, and I said, how many users you got? 1.6 billion? How many friend connections do you have? 100 and 50 billion. So, then what did I do next? A division! I divided the number of users into the number of friends connection, and the answer is 141, which is really close to 150. An amazing output!”

Dunbar’s number explains why Reed’s Law does not hold.

Reed’s Law posits that the utility of large networks grows exponentially as 2n, by considering every possible group and subgroup combination within a network. It suggests that each new member creates numerous new potential groups and subgroups, vastly expanding the network's utility. For instance, in a network of five people, Reed’s Law would include every possible grouping: pairs, trios, quartets, and so forth, resulting in 25 - 1 = 31 possible groups. As the network grows, the number of these potential groups grows exponentially.

The problem is, people and organizations do not function this way, in part because they simply can’t. Think of the people that you know. Do you regularly communicate in groups of every single possible combination and size? With 100 friends, family, and acquaintances, you would belong to 1,267,650,600,288,230,000,000,000,000,000 - 1 groups, clubs, and networks!

Reed’s theory is a math problem that can be solved on paper but fails in reality because it overlooks practical and cognitive limitations.

Maintaining every possible group and subgroup is not feasible due to the physical and mental limits of being human. While adding members theoretically increases the number of possible connections and groups, managing and maintaining meaningful interactions within these groups becomes unsustainable. The exponential growth in network utility Reed’s Law predicts is stunted by our cognitive boundaries as well as other practical connectivity considerations.

For Bitcoin, this means that the network effect has some limits.

Although in theory, users can interact with each other, in practice it is more likely that they only interact with 150-200 connections.

Now, in financial transactions, it is not always necessary to know the counterparty. In most stock trades for example, the parties have no knowledge of each other. Bitcoin, with its pseudonymous protocol, facilitates this arrangement by design. So it’s likely that the practical limit can be much larger than 200. Still, people don’t typically transact with 15

others anywhere in the world; they transact within the financial market ecosystem that is close or convenient to them.

Exclusion costs refer to the expenses or losses incurred when an entity is excluded from a network or marketplace. These costs can manifest in various forms, such as missed opportunities, reduced market share, or diminished user engagement. Understanding exclusion costs is particularly crucial in the context of network effects, where the value of a product or service increases as more people use it.

Exclusion costs are typically opportunity costs. Opportunity cost represents the value of the next best alternative that is foregone when a decision is made. It is not incurred directly but is a crucial concept in assessing the relative profitability or utility of different choices.

For instance, consider a business that has $1 million to invest. If the company decides to invest this money in Project A, the opportunity cost is the potential return it could have earned from investing in Project B, which is the next best alternative. If Project B could have yielded a return of $200,000, this amount represents the opportunity cost of choosing Project A over Project B. Representing “what might have been,” opportunity costs are ingrained in every decision we make. Resources (time, money, effort) are limited, and choosing one option usually means forgoing others. Understanding opportunity costs helps individuals and businesses to better allocate their resources by considering the potential benefits of alternative options.

For instance, consider a new social media platform trying to compete with an established giant like Facebook. The exclusion cost for potential users who do not join the established network is significant: they miss out on the vast connections and interactions available to users within the network. This can lead to a vicious cycle where the network effect reinforces the dominance of the incumbent platform, making it even harder for new entrants to attract users.

From a business perspective, exclusion costs can also impact firms that are unable to participate in a dominant network. For example, a seller excluded from a major online marketplace like Amazon may face significant exclusion costs in terms of lost sales and reduced visibility.

These costs are exacerbated by the network effect, as the marketplace’s value is largely driven by its large user base. Sellers outside the network miss out on access to this extensive customer base, leading to lower revenues and potential business decline.

Exclusion costs also play a crucial role in the dynamics of twosided markets, where platforms connect two distinct user groups, such 16

as buyers and sellers or service providers and consumers. Take Uber, for example: drivers and riders benefit from being part of a large network. If a driver is excluded from Uber’s platform, they incur exclusion costs by losing access to a vast pool of potential customers. Similarly, riders excluded from the platform face higher wait times and potentially higher prices due to a smaller pool of available drivers.

Early adopters benefit from the first mover advantage and rapid growth. The value of the network increases at an increasing rate, and this value accrues to the users. Being an early member of the network is an advantage. Early users join the network to gain this advantage.

For those not in the network, the cost of self-exclusion grows as the network value grows. Not being in the network becomes a disadvantage. The nature of the network effect changes slightly. The value of the network increases at a decreasing rate. But rather than join the network to gain an advantage, late users join the network to shed the disadvantage of not being in the network.

At some point, the network’s value is so great that the exclusion cost becomes unbearable. Even if the network user is no longer benefiting from network effects, the threat of economic harm is so great that the user feels compelled to stay. At this point, the exclusion cost is more direct than opportunistic. The user may even hate the network that they are a member of, and this has already manifested in networks like social media, banks, and political groups.

Here, Facebook again serves as a great example. Public sentiment towards Facebook has been increasingly negative in recent years, with several surveys and studies highlighting the dissatisfaction and distrust many users feel towards the platform.

Recent research suggests there is a noticeable decline in user engagement and sentiment towards Facebook. A survey indicated that 48% of respondents reported a sharp decline in referral traffic from social media sites, with Facebook being a significant contributor to this drop.

This decline has led many publishers to focus more on direct channels and alternative platforms such as WhatsApp and Instagram, as they perceive Facebook to be less beneficial for their business needs.

Additionally, a broader sentiment analysis indicates a significant portion of users harbor negative feelings towards Facebook. A Reuters Institute’s survey revealed that publisher sentiment towards Facebook has worsened, with many expressing concerns about declining advertising revenues and the platform's role in spreading misinformation and other harmful content. This growing dissatisfaction is prompting

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publishers and businesses to reconsider their reliance on Facebook and explore other platforms that may offer better engagement.

Furthermore, academic studies on sentiment analysis have consistently shown mixed to negative feelings towards Facebook. Users frequently express frustration over privacy issues, data misuse, and the platform’s impact on mental health. The negative sentiment is also reflected in discussions and reviews on various forums and social media channels, where users criticize Facebook’s policies and its handling of user data.

Debanking, the practice of financial institutions terminating or restricting services to certain customers, has gained considerable attention in recent years, with JPMorgan Chase & Co. (Chase Bank) being one of the prominent banks involved in such practices. Debanking by Chase Bank has raised significant concerns regarding its impact on individuals and businesses, particularly focusing on the network exclusion costs associated with such actions.

Debanking typically involves a bank closing a customer’s account or restricting their access to financial services without providing a clear reason. Chase Bank, one of the largest financial institutions in the United States, has been reported to engage in debanking practices, affecting various customers, including political activists, cryptocurrency businesses, and individuals flagged for potential compliance risks.

The rationale behind debanking can vary. Banks like Chase may cite regulatory compliance, risk management, and the need to prevent illegal activities such as money laundering or fraud. However, the opaque nature of these decisions often leaves customers with little recourse or understanding of why they were targeted, leading to significant financial and personal disruptions.

Imagine what your life would be like if you could not operate with the assistance of the banking system. Confined solely to cash, what would your life be like in terms of routine functions like buying food, shelter, and transportation? Living outside the banking system presents a multitude of challenges that affect nearly every aspect of daily life. The integration of financial services into modern society means that exclusion from these services can lead to significant economic, operational, social, and psychological difficulties.

One of the primary economic challenges faced by individuals without bank accounts is the lack of secure storage for their money.

Without access to bank accounts, individuals are forced to keep their cash in insecure locations, increasing the risk of theft or loss. Additionally, managing income and expenses becomes cumbersome. Many employers prefer or require direct deposit for wages, leaving unbanked individuals reliant on expensive and inconvenient alternatives such as 18

check-cashing services. These services charge high fees, reducing the net income available to the individual and compounding financial instability.

Living without a bank account also imposes significant operational and logistical burdens. Basic financial transactions, such as paying bills, become more complicated and time-consuming. Unbanked individuals often need to travel to multiple locations to pay bills in cash, which is both impractical and inefficient. The absence of a bank account also means missing out on the benefits of digital financial services, such as online banking, automated bill payments, and electronic transfers, further complicating financial management.

The social and psychological impact of being unbanked can be profound. There is often a stigma associated with not having a bank account, which can affect personal and professional relationships. The perception of financial instability or irresponsibility can lead to social isolation and reduced opportunities for advancement. Moreover, the stress and anxiety associated with managing finances without the safety and convenience of a bank account can take a toll on mental health, contributing to a cycle of financial and emotional instability.

Debanking is an immoral exclusion cost because it is unbearable, extrajudicial punishment. In today’s digital age, being excluded from the banking system means being excluded from society at large. Shopping, payments, and virtually all communication of every time requires some type of interaction with the banking system.

Any exclusion limits access to goods and services and isolates individuals from the normalcy enjoyed by others.

Networks with centralized control structures become keenly aware of network power and exclusion costs. They use this to their advantage to control, coerce, and manipulate the network and its users in a way that benefits the central authority.

Faced with an unbearable cost of exclusion, users can do nothing. They are “locked-in” to a system that may not necessarily benefit them all the time. In some cases, continued participation in the network can be economically or socially harmful.

One significant cause of network lock-in is the lack of interoperability. This is frequently found in computer data and communication systems. When such systems are not designed to work seamlessly with others, users face substantial barriers to switching networks. This lack of interoperability means that data, services, and user experiences are confined within the network, making the transition to alternative systems costly and cumbersome. The result is a captive user base, with limited

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alternatives and perpetually dependent on the centralized network for essential services and connectivity.

Such technical problems are typically solved eventually, because a single network maximizes value. However, dominant networks, aware of the unbearable cost of exclusion, tend to behave as dictators. If a user becomes disfavored, the network administrator can punish the user in a way that has genuine economic harm. In the realm of finance and economics, this manifests in debanking and economic sanctions. In the realm of social media, it is deplatforming. In religion, it is known as excommunication.

Users caught in network lock-in face limited alternatives and become increasingly dependent on the network, creating a cycle of dependency that is challenging to break. Groups of discarded and shunned users may attempt to build an alternative network, and often succeed initially.

The US emerged post-WWII as the world’s dominant economic power. The US dollar serves as a prime example of lock-in on a global scale, exhibiting characteristics of centralized control and dependency akin to those found in network theory. The dollar’s dominance has been entrenched through historical agreements and strategic economic policies, making it difficult for other currencies to replace it and for countries to opt out of the dollar-based system.

In 1944, the Bretton Woods Agreement was established against the backdrop of a world in ruins. Europe and Asia lay devastated from the war, while the United States emerged largely unscathed, boasting the only viable economy capable of spearheading global reconstruction.

With its substantial gold reserves and economic power, the US extended an offer to rebuild the shattered economies of Europe and Asia. However, this offer came with a significant condition: nations had to align themselves with either the US or the USSR. The Bretton Woods system codified this agreement, anchoring the world’s economy to the US dollar, which was itself pegged to gold at $35 per ounce. This arrangement made the US dollar the dominant global currency. The prospect of exclusion from this network, which would have entailed prolonged economic hardship and poverty, compelled most nations to opt for the US dollar-dominated framework. The dollar was the Schelling point.

The Bretton Woods system ended in 1971 when President Richard Nixon ended the dollar’s convertibility to gold, effectively moving to a fiat currency system. History claims the decision was driven by the need to address the trade deficits and inflation that had begun to undermine confidence in the dollar’s fixed value. The real reason is that there is not enough gold in the world to serve as backing for the transaction volume 20

of a growing network of international trade. Remember, network values grow quadratically, and by 1971, the value of global economic transactions made gold infeasible as a store of value to back the dollar. A new commodity was needed.

In the aftermath, the US sought new ways to maintain the dollar’s dominant position. A critical development was the US-Saudi petrodollar arrangement established in the mid-1970s. Under this arrangement, Saudi Arabia agreed to price its oil exports exclusively in US dollars and invest the surplus oil revenues in US Treasury bonds and other dollar-denominated assets. In return, the US provided military protection and economic support to the Saudi regime.

This petrodollar system extended the dollar’s dominance by ensuring that global oil trade, the largest and most crucial commodity market, was conducted in dollars.

Every country needs oil. At a minimum, 100 million barrels of oil are consumed each day. At the height of the global COVID lockdowns, when transportation and energy was limited to essentials like farming, food distribution, emergency services, and such, the world was still consuming 80 million barrels of oil per day. Below this level, countries don’t just suffer, they begin to die.

Countries which need to purchase oil–that is, every country in the world–must hold substantial dollar reserves. This forces a constant demand for the dollar. This arrangement benefits the United States in an exceptional way, by lowering the level of interest rates. This in turn facilitates faster growth, which increases the value of the dollar. This feedback loop was intentionally designed to maintain the dollar’s indispensable role in the global economy.

The arrangement not only locked countries into reliance on the dollar for energy needs but also tied their economic stability to the US financial system. Whereas feedback loops help networks grow big, lockin ensures that networks stay big and stay dominant. Countries with dominant currencies can impose their will on other countries, because they control the access and flow of money. In the case of the US dollar, they also control access to energy.

New fossil fuel extraction technologies along with the discovery of ample shale reserves in the United States meant that the US reliance on Saudi oil dominance was no longer needed. Likewise, US development in the area of cold fusion seems to indicate that the US has viable capabilities for long-term energy independence. Schelling-point network effects can keep the dollar dominant for a long time. Accordingly, the US and Saudi Arabia have abandoned the petrodollar system.

Other countries, eager to break free from the lock-in effects, view this as an opportunity and are looking at alternative currency

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systems. The Digital Euro and a BRICS4 currency system are just two examples. The principles of network economics say that these currency forks will gain some initial traction, then languish. Some may fail outright.

If the dollar network exemplifies lock-in, Bitcoin is potentially the key that opens the lock. Unlike a Digital Euro or BRICS currency, Bitcoin is a first mover with an established global presence.

It is not hard to see why some governments, and particularly the US government, would view Bitcoin as a threat to that dominance. Consider again the case where Bitcoin was used to quickly send money to Ukraine in 2022 to provide military and humanitarian support, often within hours. The speed and volume with which money was sent, absent any controls or intermediary, was unprecedented in human history.

While most in the West view this as a ‘good thing,’ it begs the question: could not such money flow just as easily to the West’s enemies? And of course, the answer is “Yes.” In fact, it did.

Bitcoin and other cryptocurrencies present a significant challenge to the traditional framework of economic sanctions against antiWestern countries. Historically, the United States and its allies have leveraged the U.S. dollar’s dominance to impose effective economic sanctions by controlling access to the global financial system. Countries like Iran, North Korea, and Venezuela have faced severe restrictions on their access to international banking systems and trade networks.

However, cryptocurrencies provide sanctioned countries with a means to conduct international trade and financial transactions without relying on the dollar or traditional financial institutions. It’s not even necessary to use established assets like Bitcoin for transactions. Countries may, at any time, build a closed blockchain system and transfer money between themselves and their friends in the global dollar network. The ability for anyone to build a currency system from nothing, and practically on demand, is a fundamental disruption to conventional financial economics.

The widespread adoption of Bitcoin could weaken the demand for the dollar in several ways. As more countries and entities turn to cryptocurrencies for international trade and finance, the reliance on the dollar decreases, diminishing its network power and status as the world's primary reserve currency. The U.S. government’s ability to control and monitor international financial transactions is reduced in a world where

4 BRICS is an intergovernmental organization comprising Brazil, Russia, India, China,

South Africa, and expansion members Iran, Egypt, Ethiopia, and the United Arab Emirates.

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cryptocurrencies are widely used, weakening the leverage that the U.S. has traditionally enjoyed through its financial hegemony.

Countries may choose to diversify their reserves by holding Bitcoin alongside traditional currencies, reducing their dependency on the dollar and protecting them from potential U.S. economic policies that could negatively impact their economies. As the utility and adoption of cryptocurrencies grow, market sentiment towards the dollar could shift.

If investors and governments perceive Bitcoin as viable alternatives to the dollar, they may reallocate their assets, potentially leading to a depreciation of the dollar’s value.

Whether digital platforms, communication systems, or even social structures, there’s a compelling case for consolidation. Imagine a world where instead of numerous small, disconnected networks, we have a single, unified system. This consolidation can dramatically increase the total value created for all participants.

The United States was an early example of a unified political network. Before unification, each colony operated largely independently, with its own governance, laws, and economic systems. This fragmentation led to inefficiencies, conflicts, and limited growth potential. By coming together under a single federal system, the United States was able to harness the power of network effects in governance and commerce.

The Constitution established a common legal and political framework, acting as a standardization mechanism. This allowed for free movement of people, goods, and ideas across state lines, dramatically increasing the potential for interaction and value creation. The elimination of internal trade barriers created a large, unified market that spurred economic growth and innovation.

The federal system also allowed for economies of scale in areas like national defense and diplomacy. Instead of each state maintaining its own army or conducting foreign policy, these functions were consolidated at the federal level, reducing redundancy and increasing effectiveness.

Eventually, the United States adopted a common currency and built interconnected transportation and communications networks. Europe, discussed later, stands in stark contrast to this arrangement.

Network consolidation also brings significant economic advantages. With a larger user base, the fixed costs of running the network –things like infrastructure, development, and maintenance–are spread more thinly. This economy of scale allows for greater investment in improving the network’s capabilities and user experience.

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Standardization is another key benefit. When a single network dominates, it naturally establishes universal standards. This eliminates the headaches of compatibility issues and reduces the friction of interaction between users. Everyone speaks the same language, so to speak.

The consolidation of data into a single network can lead to powerful insights and improvements. With more data to analyze, the network can offer better personalization, more accurate recommendations, and continually refine its services based on a comprehensive understanding of user needs and behaviors.

Finally, a unified network can more easily achieve global reach.

It can break down geographical barriers, enabling communication and interaction on a truly worldwide scale. This universal accessibility creates value through its sheer ubiquity and the diverse connections it enables.

In essence, by bringing users, resources, and innovation into a single network, synergy is created—the whole that is greater than the sum of its parts. The total value generated often far exceeds what would be possible with multiple fragmented networks, as it harnesses the full power of network effects while eliminating the inefficiencies of fragmentation.

The Euro serves as a great example of network consolidation within the economic sphere. Introduced in 1999 and officially launched in 2002, the Euro was adopted by 19 of the 27 European Union (EU) member states, collectively known as the Eurozone. This unification of currency was aimed at fostering economic integration, facilitating trade, and enhancing economic stability across Europe. To fully understand the impact of the Euro, it is essential to explore the conditions before and after its adoption.

Before the Euro, each European country had its own national currency, such as the German Deutsche Mark, the French Franc, the Italian Lira, and the Spanish Peseta. This fragmented system created several challenges for both businesses and consumers.

Each currency fluctuated independently in value, creating uncertainty and risk for businesses engaged in cross-border trade. Exchange rate volatility could significantly impact the cost of imports and exports, making it difficult for businesses to plan and price their products competitively.

Travelers and businesses faced additional costs related to currency conversion. Every time a currency needed to be exchanged, banks and currency exchange services charged fees, which added up, especially for frequent transactions.

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The lack of a common currency made it difficult to compare prices directly across different countries. This lack of transparency sometimes led to price disparities and reduced competition.

Each country had its own central bank and monetary policy, leading to a lack of coordination in addressing economic issues. Countries responded to economic challenges independently, which sometimes resulted in conflicting policies that could exacerbate regional economic instability.

However, the primary reason for a unified currency was to make the Eurozone more competitive in the global economy. By adopting the Euro, member states aimed to streamline cross-border trade, eliminate currency exchange risks, and reduce transaction costs. This economic integration was designed to enhance price transparency, stimulate competition, and attract investment. Additionally, a unified currency facilitated more coordinated monetary policies through the European Central Bank, promoting economic stability and resilience. The Euro’s introduction aimed to solidify the Eurozone’s position as a formidable economic bloc, capable of competing with major global economies like the United States and China.

Was this transition successful? The U.S. dollar remains the most traded currency globally, accounting for about 88.5% of daily forex transactions. This is due to its role as the world's primary reserve currency and its use in pricing many commodities like oil and gold. The euro is the second most traded currency, making up roughly 30.5% of daily forex transactions.5 Its popularity is attributed to the economic clout of the Eurozone.

Metcalfe’s Law states that the value of a network is proportional to the square of the number of connected users in the network. The Rule of 2 states that the percent change in value is twice the percent change in users. This is the first corollary6 to Metcalfe’s Law. The second corollary is: a single network maximizes value.

Let’s assume two networks, A and B. Network A gains users from 0 to 100. Network B starts with 100 users and loses over time. The value of both networks is:

5 The percentages for the most traded currencies do not add up to 100% because each

currency is counted in every transaction it is involved in. In the foreign exchange market, a trade always involves two currencies. For example, in a trade between the US dollar (USD) and the Euro (EUR), both currencies are counted. This results in the total percentage being higher than 100%.

6 A corollary is an inference or deduction that follows directly from a previously proven

statement or proposition, often requiring minimal additional proof.

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When comparing the values of networks A and B, an interesting characteristic emerges: the total ecosystem value fluctuates depending on the distribution of users. However, the maximum value is achieved when one network monopolizes the user base. For instance, with 100 users, the value of a single unified network (either network A or network B with 100 users) is 4950, whereas splitting the users between two networks results in lower total value.

Human behavior plays a critical role in network economics. Users inherently seek to maximize their utility and wealth, which drives them to gravitate toward larger networks. This behavior is driven by several factors: 1. Network Effects: As more users join a network, the benefits of being part of that network increase for each member. This creates a positive feedback loop, attracting even more users.

2. Exclusion Costs: Users of smaller networks face higher exclusion costs, as they miss out on the benefits and connections available in larger networks. This incentivizes them to switch to larger networks.

3. Lock-In: Once users join a large network, the cost of switching to a smaller, less valuable network is prohibitive. This lock-in effect further consolidates the dominance of the larger network.

If the networks are incompatible, users must typically make a choice. In a mutually exclusive environment, these dynamics create a feedback loop where the largest network continuously attracts more users at the expense of the smaller network. There is a second, negative feedback loop where the smallest networks lose users. This is the network effect in reverse, and smaller networks lose value at an ever-increasing rate until it levels off—a backwards S-curve.

Eventually, the larger network is elevated to a position of absolute dominance and the smaller network is relegated to a position of irrelevance.

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This dynamic theoretically favors the creation of monopolies, as users gravitate towards the largest network to maximize their utility.

However, in practice, many markets exhibit duopolies rather than monopolies.

Different user preferences and needs can lead to market segmentation. For example, users may prefer different platforms for social networking versus professional networking, allowing multiple networks to coexist and thrive. Governments and regulatory bodies may enforce anti-monopoly laws and regulations to promote competition, preventing a single network from becoming too dominant. While lock-in effects favor larger networks, switching costs can also work against a monopoly if an alternative network offers significant value that justifies the switch.

In a market with four networks, Zipf’s Law says that the top two networks will capture 72% of the market share. With eight networks, the top two still capture a majority with 55%, which leaves most competitors with less than 10% share each. So, after the first three or four entrants are established, the dominant network loses little and the challenger gains little. This helps explain why, in most ecosystems, there are rarely more than four major telecom companies, supermarket chains, airline companies, or computer operating systems.

The COVID-19 pandemic catapulted video conferencing systems into the forefront of everyday life for businesses, educational institutions, and social interactions. Before the pandemic, platforms like GoToMeeting and Webex held significant market shares, catering primarily to corporate clients with established remote meeting needs. But like Doom which gave away its software, Zoom’s freemium model attracted a large number of users who could use the basic features for free, which helped drive adoption.

Both Zoom and Teams benefitted from Lazy User / Schelling Point behavior, capitalizing on minimal setup and simplicity of use. People joined Zoom primarily because someone else was using it, and the software is required for all parties to participate in the meeting. Zoom quickly went through the feedback loop of users recruiting new users due to necessity rather than choice. And of course, once a critical mass was reached, virality of adoption was assured.

Microsoft Teams grew differently. Taking advantage of the preexisting widespread adoption of Microsoft Office (and particularly the email program Outlook), Teams piggybacked on lazy user tendencies to grow. In much the same way that the telegraph spread through the existing network of railroad, or that Bitcoin spread through the existing

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network of the internet, Teams built a new network on top of an existing, dominant network.

As of 2023, the market share of videoconference providers was:

The market share results don’t perfectly align with Zipf’s Law— Zoom and Teams have more than would be predicted. The likely explanation is that there is probably still some residual carryover from the COVID effect. Still, the top two have a greater than 10% share each, while the remainder all have less than 10% share each, which is consistent with Zipf’s Law.

In a general sense, a fork is the creation of new, competing networks that challenge the dominance of the original network. Community disagreements often ignite the spark for a fork. These debates can become so polarized that they fracture the community, leading to the creation of a new, independent network.

Twitter’s dominance, and subsequent dictatorial behavior, is an excellent example of this. Before Elon Musk’s acquisition in 2022, Twitter’s conduct often raised concerns about dictatorial behavior. During the 2010s and early 2020s, the platform’s content moderation and user management sparked debates over free speech and censorship. Infamous high-profile bans highlighted Twitter’s crackdown on certain political ideologies. Critics argued that the selective enforcement and lack of transparency in decision-making processes contributed to a sense of unfairness and mistrust. This perception of centralized, unaccountable control fueled calls for reform and greater transparency in social media governance.

Attempts at alternatives to Twitter proliferated: MeWe (2012), Minds (2015), Gab (2016), Mastodon (2016), Parler (2018), CloutHub (2018), Nostr (2020), Gettr (2021), Bluesky (2021), and Truth Social (2022).

Such competing networks almost always fail because they lack first mover status, are therefore smaller, do not interact with the 28

dominant network, and ultimately offer significantly less value. Forks introduce fragmentation, which dilutes network effects. The value proposition–that a single network maximizes value for all–is explained later.

The end result is this: the lack of alternative networks with comparable value reinforces the central authority’s control and facilitates dictatorial behavior on the part of the network administrators. Hence boycotts and competition, which were successful methods to implement change in the production economy of the 20th century, of almost entirely ineffective in the 21st century information economy.

The concept of Nash equilibrium,7 where no player has an incentive to unilaterally change their strategy given others’ choices, applies strongly to Bitcoin’s dominance. Users and investors are inclined to hold and transact in Bitcoin because of its widespread adoption, creating a self-reinforcing cycle. Switching to an alternative cryptocurrency would, in most cases, not improve their outcomes, thus maintaining the equilibrium.

The 2017 Bitcoin scalability debate provides a compelling case study of these game theory concepts in action. The scalability debate centered on how to increase the Bitcoin network’s transaction capacity amidst rising popularity and transaction volume. This transaction capacity was codified in the programming; a change required the consensus of the network.

As the community faced decisions about addressing scalability issues, stakeholders had to choose between two main solutions: 1.

2.

The “big block” approach, advocating for increased block sizes to reduce transaction fees (eventually becoming Bitcoin Cash).

The Segregated Witness (SegWit) solution, proposing to enhance scalability without altering block sizes.

This scenario resembled a coordination game akin to the Prisoner’s Dilemma. 8 Cooperation meant all players agreeing on one

7 A Nash equilibrium is a concept in game theory where no player can benefit by changing

their strategy while the other players keep theirs unchanged. Named after mathematician John Nash, this equilibrium occurs when each player's strategy is optimal given the strategies of all other players. In other words, in a Nash equilibrium, every participant's decision is the best they can make, taking into account the decisions of others. This concept applies to various fields, including economics, politics, and evolutionary biology, helping to predict the outcome of strategic interactions in competitive environments.

8 The Prisoner's Dilemma is a standard example of game theory that demonstrates why two rational individuals might not cooperate, even if it appears that it is in their best interest to do so. In this hypothetical scenario, two prisoners are accused of a crime and interrogated separately. They have the following choices: if both prisoners cooperate with

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solution, keeping the chain united. Defection involved supporting a hard fork.9 The August 2017 hard fork resulted in the creation of Bitcoin Cash (BCH), with advocates of larger blocks choosing to pursue their vision of scalability. However, the majority of stakeholders continued to support the original Bitcoin chain, reinforcing its status as the focal point or Schelling point in the cryptocurrency ecosystem.

The creation of a fork creates two competing networks, like the A and B example previously. A world with two competing networks is suboptimal, meaning all users would be better of if they just picked one network. The creation of Bitcoin Cash harmed the Bitcoin ecosystem, but because the Bitcoin Cash network is considerably smaller, the loss to Bitcoin is not fully recouped by the new market value of BCH. Using the Rule of 2 and recent market capitalization values for Bitcoin and BCH, it can be estimated that for every 12 Bitcoin users there is one BCH user (though some may hold both). This is akin to the A and B table above where A (representing BCH) and B (representing Bitcoin) are at 10 and 90 respectively. If all BCH users were able to instantly sell BCH and buy Bitcoin, the value of the total ecosystem would rise from 4140 to 4950, a gain of 20%. This would increase the value of Bitcoin by twice the market capitalization of BCH. This simple example shows that a unified Bitcoin network would have a significantly higher value than that of the fragmented networks combined. Bitcoin forks, such as Bitcoin Cash (BCH) and Bitcoin SV (BSV), undermine the ecosystem’s value by creating competing, incompatible networks. This fragmentation dilutes the user base, reduces network effects, and hampers overall growth and stability. The larger network would benefit from stronger network effects, reduced exclusion costs, and a more potent lock-in effect.

The consolidation in the banking industry over the past few decades serves as a compelling illustration of how network effects can maximize value in a single network. The attached image and accompanying text highlight the significant mergers and acquisitions that have shaped the current landscape, leading to the dominance of the “Big Four” banks: JP Morgan Chase, Bank of America, Wells Fargo, and Citigroup. This

each other and remain silent, they each get a short sentence. If one betrays the other while the other remains silent, the betrayer goes free while the silent prisoner receives a long sentence. If both betray each other, they both receive a moderate sentence. The dilemma illustrates that although mutual cooperation would lead to a better overall outcome, rational self-interest leads both prisoners to betray each other, resulting in a worse outcome for both.

9 Hard forks are software changes incompatible with previous versions of Bitcoin.

The result in the creation of a new cryptocurrency, while Bitcoin continues on its original blockchain.

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consolidation underscores the economic and operational efficiencies achieved when smaller, fragmented entities combine to form larger, more dominant networks.

Between 1990 and 2010, 37 banks consolidated into the four major players we see today. This period saw a significant wave of mergers, particularly during the 2008 Financial Crisis, when weaker banks were absorbed by stronger ones. For instance, JP Morgan Chase emerged as a behemoth by acquiring Washington Mutual and Bear Stearns, while Bank of America expanded its footprint by taking over Countrywide Financial and Merrill Lynch.

Why hasn’t this coalescence occurred in cryptocurrency? Perhaps in time it will. It took Europe 400 years to move from the thaler to fragmented currencies then back to a single currency—the Euro.

What restaurant is typically regarded as the world’s most successful? Most would say McDonalds. Now think about this:   

Does McDonald’s produce the best tasting food?

The healthiest food?

Even the cheapest food?

Most would say “No.” So none of the attributes that one would rationally associate with a successful restaurant are present. Yet the McDonald’s model permanently changed human behavior and expectations about food globally and for decades.

The fallacy is the perception that a network must inherently possess superior attributes to succeed or have value. This misconception overlooks the characteristics of network effects that we’ve discussed in the chapter: first mover status, feedback loops, Schelling points and lazy users, exclusion costs, lock-in, and value maximizing behavior.

McDonald’s exemplifies this misconception. It wasn’t the quality of their hamburgers that made them an iconic brand, but rather their strategic positioning and innovation in service speed. McDonald’s didn’t invent the drive-through, the hamburger, nor the fast-food chain, but they revolutionized how food was delivered to customers, particularly during a pivotal moment in American history.

In the 1950s, the United States was undergoing significant transformation with the expansion of the Eisenhower Interstate Highway System. This new network of roads connected cities and towns across the nation, fostering increased mobility and car travel. McDonald’s saw an opportunity in this expanding infrastructure. They understood that as people traveled more, they needed convenient and quick meal options.

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This need dovetailed perfectly with McDonald’s business model of fast service and standardization.

What McDonald’s offered was speed. Post-war America was increasingly mobile over long distances. You must fuel your car, but you also must fuel your body, and time is money. Their drive-through service was a new concept at the time. It catered perfectly to the on-the-go lifestyle of American families and travelers. The ability to quickly grab a meal without leaving the car was a significant advantage that McDonald’s capitalized on. This focus on speed and convenience resonated with the public, aligning seamlessly with the increasing car culture of the era.

The placement of McDonald’s restaurants along these highways was no coincidence. It was a strategic move to leverage the network effects of ground transportation. Highways facilitated easier travel, and McDonald’s provided a predictable, reliable stop for travelers. This symbiotic relationship between the highway system and McDonald’s locations created a feedback loop of increasing utility and value for both.

The success of McDonald’s became so pronounced that it influenced the social and economic landscape of American towns. A town’s status and visibility were significantly enhanced by the presence of a McDonald’s restaurant. This phenomenon was especially evident in the era of physical road atlases. Due to limited space, not every small town could be featured on these maps. However, the inclusion of a McDonald’s often guaranteed that a town would be “put on the map,” both literally and figuratively. The presence of a McDonald’s signified that a town had reached a certain level of development and connectivity, making it a noteworthy stop for travelers.

Bitcoin’s critics often highlight its limitations: slow transaction processing, limited transaction throughput, high fees during peak times, and the complexity of use. So what? These criticisms miss a crucial point: network effects matter most, and the network effect is almost exclusively a size-driven phenomenon.

Bitcoin’s value doesn’t depend on being the most efficient or user-friendly cryptocurrency. Bitcoin’s true strength lies in its firstmover advantage and the network effects it has generated. This innovation came at a pivotal moment when (a) digital, mobile, wireless communication was taking off, and (b) post-Great Recession, trust in conventional financial institutions was waning.

Bitcoin capitalized on the growth of the internet and digital infrastructure in the same way that McDonald’s leveraged the expanding Eisenhower Interstate Highway System to position its restaurants for maximum convenience. The internet provided a new way for people to

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interact, trade, and conduct business, and Bitcoin offered a currency that fit within that digital landscape.

Bitcoin was first, and it enjoys the first mover advantage and the quadratic network growth that comes with it. It is a convenient Schelling point for the lazy user, the original textbook that new users learn from, and the template upon which new blockchain innovation is based.

Bitcoin’s feedback loop of users and price appreciation that attracts new users is not a flaw, but a predictable element associated with network effects.

First movers become final winners. Being first means being biggest. And being biggest means Bitcoin dominates all other cryptocurrencies and, in all likelihood, always will. In time, it is entirely possible, perhaps predictable, that Bitcoin will overtake the market values of fiat currencies or gold.

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To prove mathematically that for k networks, a single network maximizes the value of the total ecosystem given by 𝑉=

𝑛 × (𝑛 − 1) 2

we need to compare the total value V for different configurations of networks.

V1: Total value when there is a single network.

Vk: Total value when there are k separate networks.

When there are k separate networks, let n1, n2,…, nk denote the number of nodes in each network respectively. The total number of nodes across all networks is n = n1 + n2 +…+ nk. The total value V for k separate networks is the sum of values for each network: 𝑛 × (𝑛 − 1) 2

𝑉 =

To prove that a single network maximizes V compared to k separate networks, we need to show that V1 ≥ Vk. Jensen’s Inequality10 can be applied to the concave function f(x) = x ⋅ (x − 1) / 2: 1 𝑘

𝑓(𝑛 ) ≤ 𝑓

1 𝑘

𝑛

However, since we are looking at the sum directly, we use: 𝑛 =𝑁

𝑉 =

×(

)

≥∑

×(

)

Thus, the total value of the ecosystem when all nodes are combined into a single network is always greater than or equal to the sum of the values when nodes are split into multiple networks.

10 The inequality essentially says that the value of a convex function at the weighted av-

erage of several points is less than or equal to the weighted average of the function's values at those points. This property is particularly useful in various fields, including economics, probability theory, and optimization.

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