Blockchain Token Economic Models and Markov Equilibrium

Can stability and growth occur in the same variable at the same time?

A blockchain is a peer-to-peer network. A blockchain is a distributed cryptographic ledger communicated by all participating nodes and records every data or transfer of funds. The transactions are collected in blocks discovered through a protocol-generated random process. Some blockchains include cryptographic tokens, while others do not.

A utility function of an agent in the context of cryptographic assets would be dependent on the number of tokens in circulation in the blockchain, demand, which is the aggregated drives of agents or entities, network characteristics (security, vulnerability, delay), and incentives to verifiers (miners, validators, stakeholders, delegates, enough token holders, etc.)

Economic equilibrium occurs when market forces such as supply and demand are balanced. Market equilibrium is defined in this context as a condition in which a market price is formed through competition such that the quantity of goods or services requested by buyers equals the number of goods or services generated by sellers.

This is known as the competitive or market clearing price, which is unlikely to alter unless demand or supply changes and the quantity is known as the “competitive quantity” or market clearing quantity. The concept of equilibrium, however, also applies in economics to imperfectly competitive markets, where it takes the form of a Nash equilibrium.

Coins as a Medium of Exchange

Coins are the required exchange vehicle for transactions and business operations on blockchain platforms due to protocol design or because they provide a higher convenience yield than alternative currencies.

The benefits of using such coins grow as the number of blockchain users grows. As a result, the coin price reflects the community’s future growth and rises if the expected user-base growth is greater. Taking a step back, when platform technology is expected to improve, enticing more agents to join the community, the resulting expectation of coin price appreciation influences agents’ current decision to participate in the community and hold coins.

Markov Equilibrium

The existence of coins as a native currency not only serves technological purposes, as practitioners argue, but, more importantly, advances the growth of the user base through agents’ expectation of future technological progress, larger user base, and higher coin price.

The model equilibrium features an intertemporal complementarity of the user base — the expectation of more users in the future feeds into more users today.

The entrepreneur’s value in the Markov equilibrium is a function of the current platform productivity and token supply, which are the two state variables.

Nevertheless, a unique non-degenerate Markov equilibrium exists under the usual conditions of the continuous-time formulation. We focus on Markov equilibria and first study agents’ decision to hold coins.

Price Formula

The coin market clearing condition offers a coin price formula, which usually increases in the size of the blockchain user base — the larger the ecosystem is, the higher the trade surplus individual participants can realize by holding coins. From an asset pricing perspective, such model is the first to provide a theoretical foundation for the valuation-to-user base ratio commonly used in the technology industry, especially for firms whose customer base feeds on network effects.

The coin pricing formula suggests a Markov equilibrium exists with the common blockchain productivity being the only aggregate state variable. Note that aggregate wealth is not an aggregate state variable, because we are not clearing the goods market. This is consistent with many ICOs that fix the supply of tokens. Note that agents can incur in negative consumption, and storage technology is always available for agents to transfer wealth over time.

These assumptions are reasonable because the coin market is relatively small and orthogonal to the whole economy. Anything that happens in the cryptocurrency markets hardly has a material impact on the aggregate consumption and pricing kernel (also known as the stochastic discount factor, is the random variable that satisfies the function used in computing the price of an asset).

The state variable of the Markov equilibrium is described by the stochastic processes of agents’ choices and coin price on the filtered probability space, describing the “history of the process over time, generated by Brownian motion such that:

(1) Agents know and take as given the process of coin price;

(2) Agents optimally choose consumption and savings (invested in coins and storage);

(3) Coin price adjusts to clear the coin market, thus reaching an equilibrium price;

(4) All variables are functions of the state variable, which follows an autonomous law of motion.

The equilibrium, found through the coin pricing formula, is unique in the space of continuous and smooth functions. Consider a positive coin price at time t. Without restricting the price path to be continuous, agents can coordinate to a coin price equal to 0 and, right after this, agents can coordinate on a positive coin price again. Under a continuous price path restriction, as long as the initial coin price is positive, we have a unique, non-degenerate equilibrium with a positive coin price. Once the current coin price dynamics are given, community size can be uniquely determined.

Coin price is thus linked to the stages of platform adoption. On a logarithm scale, coin price increases fast in the early stage, and then gradually rises with the user base, but when the system has accumulated a critical mass of users, the increase of coin price speeds up and converges to its long-run asymptote. Such dynamics are qualitatively similar to Bitcoin and other cryptocurrencies.

The development path

More specifically, when blockchain technology is inefficient, the growth of the user base in response to technological progress is limited. However, as the community’s size grows, the user base’s growth feeds on itself — the more agents join the ecosystem, the greater the surplus from blockchain trading. When the pool of newcomers is depleted, user adoption begins to slow. In fact, because this model does not account for population growth, as more agents join the ecosystem, fewer newcomers will be included in the future when common blockchain productivity rises even further.

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