[Paper Review] Do Bitcoins make the world go round? On the dynamics of competing crypto-currencies

Stefan Bornholdt, Kim Sneppen|arXiv (Cornell University)|Mar 24, 2014

Complex Systems and Time Series Analysis10 references16 citations

TL;DR

This paper proposes that the value of crypto-currencies, including Bitcoin, emerges not from intrinsic properties but from social dynamics akin to fashion adoption, modeled via a voter/Moran process where agents copy each other's preferences. The key finding is that power-law distributions of market capitalization and trading volume—observed in real crypto-markets—can be reproduced by this simple model, suggesting Bitcoin’s dominance is transient and socially contingent rather than fundamental.

ABSTRACT

Bitcoins have emerged as a possible competitor to usual currencies, but other crypto-currencies have likewise appeared as competitors to the Bitcoin currency. The expanding market of crypto-currencies now involves capital equivalent to $10^{10}$ US Dollars, providing academia with an unusual opportunity to study the emergence of value. Here we show that the Bitcoin currency in itself is not special, but may rather be understood as the contemporary dominating crypto-currency that may well be replaced by other currencies. We suggest that perception of value in a social system is generated by a voter-like dynamics, where fashions form and disperse even in the case where information is only exchanged on a pairwise basis between agents.

Motivation & Objective

• To understand the emergence of value in competing crypto-currencies as a social phenomenon rather than an economic or technical one.
• To investigate whether Bitcoin’s market dominance is sustainable or merely a result of historical precedence and social adoption dynamics.
• To model the distribution of market capitalization and trading volume in crypto-markets using a minimal agent-based framework based on pairwise communication.
• To test whether the observed power-law scaling in real crypto-currencies can be reproduced by a simple voter-like dynamics with constant innovation of new currencies.

Proposed method

• A discrete-time agent-based model is used, where each agent has a fixed number of memory slots representing awareness of different crypto-currencies.
• At each time step, two agents are randomly selected, and one copies the currency preference of the other, simulating social influence through pairwise communication.
• When a currency is no longer held by any agent, it is removed and a new one is introduced at random, maintaining a constant diversity of currencies.
• The model is simulated for N=10,000 agents with D=10, 100, or 1,000 active currencies, tracking popularity, attention, and capitalization over time.
• The model uses a Moran process with birth-death dynamics to simulate the stochastic evolution of currency popularity.
• The system is analyzed for steady-state distributions of attention and capitalization, comparing them to real-world data from March 2014.

Experimental results

Research questions

• RQ1 Why does Bitcoin dominate the crypto-currency market if it is not fundamentally different from other crypto-currencies?
• RQ2 Can the observed power-law scaling in crypto-currency market capitalization and trading volume be explained by a simple social dynamics model?
• RQ3 Is Bitcoin’s dominance stable, or is it subject to replacement by other currencies through social adoption shifts?
• RQ4 How does the introduction of new currencies affect the long-term popularity and capitalization of existing ones?
• RQ5 To what extent does the observed distribution of crypto-currency values reflect a voter-like or preferential-attachment process?

Key findings

• The model reproduces a steady-state popularity distribution that scales as ∝1/x, matching the qualitative shape of real-world crypto-currency market capitalization distributions.
• The model predicts a broader distribution than observed in real data, suggesting that real markets may be subject to additional stabilizing mechanisms or preferential growth dynamics.
• Bitcoin’s dominance is not due to inherent superiority but arises from historical precedence and early adoption, making it vulnerable to replacement by other currencies.
• The total capitalization of each currency scales as ∝1/x, consistent with the observed power-law scaling in real crypto-markets.
• Trading volumes also follow a similar power-law scaling, with larger trades concentrated on more popular currencies.
• Wealth distribution among agents follows a log-normal distribution, indicating that success in the market is the result of a multiplicative process of gains and losses.