Is a Digital Token Modeled by Nash Equilibrium Possible?

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In 1950, John Forbes Nash wrote his dissertation at Princeton University on a theory of non-cooperative games outlining what would become the motivating work for his 1994 Nobel Memorial Prize in Economic Sciences. In this thesis, Nash outlines the difference between cooperative and non-cooperative games, and how a steady state can only truly occur when the self-interests of each participant are simultaneously served.

This simple observation underpins the concept of the Nash Equilibrium. It is a computational construct utilized to model a wide array of economic encounters such as the extending of credit, the conducting of political campaigns or even the development of sovereign macroeconomic policies.

But the setting in which Nash Equilibrium applies, the uncooperative game, does not adequately describe many economic systems. From global economies to local trade associations, the influence of a few significant actors supersede the natural dynamics of the interests of the collective. Even blockchain, which would appear to encourage non-cooperative conditions through decentralization, has failed to achieve it as of yet.

Take, for example, the token economies of the nascent cryptocurrencies. They have been heavily impacted by the behavior of a small, but powerful cartel of participants which aim to fix prices and coordinate price movements.

A white paper by University of Texas Professor John Griffin found that Tether was used to buy Bitcoin at key moments when it was declining. In this scenario, the self-interests of the individual participants are not simultaneously served. Only the interests of a select few are served.

Despite such failures, encouraging the non-cooperative setting in which Nash Equilibrium applies within the digital tokens landscape is possible. It requires two criteria to be met: first, a digital token must present a clear, ascertainable value to all and second, it must offer a broad appeal and adoption model.

Instilling Nash Equilibrium into a digital token, then, requires the construction of two separate stores of value. First, there must be an intrinsic store of value (such as precious metal). The economic system must be one in which the token underlies the sale and purchase of goods and services and offerings. This clear and ascertainable value encourages the capacity of the token to support the economic system. It is both intended to, and capable of, sustaining long-term participation.

Second, there must exist an extrinsic store of value which reflects the utility of the token’s role in the economic system. In other words, it must capture the value of the economic system itself, which can only grow based on participation. This extrinsic part should reflect a membership-oriented value geared towards the utilization of the token in a contained economic system. This portion, which we’ll call a “Digital Right,” is essential for securing broad appeal and adoption.

To function as a vessel of true non-cooperation, and thus Nash Equilibrium, this Digital Right must adhere to a few critical principles.

First and foremost, it can only be issued in conjunction with onboarding the physical asset into the token. Conversely, there can exist no other way to bring assets into the economic system without utilizing the Digital Right. The absence of a Digital Right would eliminate the adoption model, and thus follow the failed business model of traditional asset-pegged tokens.

Second, the Digital Right must implicitly place a value on the process of tokenizing the physical asset. The fact that it can be tokenized – that the physical asset can be encapsulated and transacted via blockchain – in itself represents a value. The Digital Right captures that value. It is therefore a persistent digital construct allowed to bear a market value. It must be a cognizable asset in its own right, not a premium on the physical asset. It can never be burned or destroyed, and should be the vehicle to take delivery of the asset or to reload the token.

Lastly, the system must be designed to intentionally limit the rate of issuance of Digital Rights over time. Such a feature encourages a natural stabilization of the pricing, discouraging cartels and other styles of coordinated behavior. The value expressed in the ecosystem is modeled by the game theoretic interaction of the independent entities responsible for bringing new assets into the network. That value is specifically expressed in the value of the Digital Right.

Combining these two attributes would create a token that could offer stability. It is a setup that would be less desirable for participation by manipulators and price fixers, and would thus be more likely well-modeled by Nash Equilibrium. Such a structure would be unlike any currently seen on the market, and would be more likely to encourage the long-term viability that so many in the crypto space currently lack.

Seth Patinkin did his PhD work in mathematics under John Forbes Nash at Princeton University and is CEO and co-founder of Ampersand Markets.

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