Source: Google

Realising Asymptotically Ideal Money

The representation of inflation in bitcoin expressed as steady and constant new coin issuance, means at any point in time, it is known how many coins will exist and when.

For example, in December 2020, approximately 88% of total coins were mined, helping create a realistic and rational expectation the existing bitcoin inventory could only sate future demand at a higher price than current.

Is Bitcoin a Reliable Medium of Exchange?

Such expectancy creates reluctance for bitcoin investors (hodlers) to spend their bitcoin, since they believe it a sensible probability they’ll be surrendering future growth in doing so.

This means as a retail money, bitcoin has disadvantages — even disregarding the settlement time not only for transactions where buyer and seller are physically present, but also the trust involved where commerce is conducted on the internet, and where transactions are not simultaneous and parties are strangers to each other — but this doesn’t mean bitcoin is an unreliable medium of exchange: a “medium of exchange” is wider than a Visa or merchant type system of adoption, where transactional efficiencies become synonymous with “scaling”.

Overcoming a Common Criticism of Bitcoin

The paradox of bitcoin idealising the “small casual transaction” and calling itself “cash” where by conventional standards it lacks the readiness and availability usually associated with “cash”, means volatility is probably one of the most cited reasons people are reluctant to transact with bitcoin — we are still uncertain what bitcoin is, if it’s trustworthy, where it came from, what value it holds, and what it is going to do next?

For example, the following graph demonstrates in a five year cycle, the fluctuations in the bitcoin price:

1 bitcoin to Sterling (source: Google)

Inverting this chart however (see below), suggests something different, whereby the volatility gets smoothed out over longer time horizons.

Realising Asymptotically Ideal Money

Asymptotically Ideal Money was conceptualised by John Forbes Nash Jr. upon realising the ideal money is free of inflation, but could prove problematic if it was so ideal it would have attractiveness for hoarding and wouldn’t circulate.

In introducing steady and constant inflation, John Nash created an asymptotically ideal money — i.e. a money that approaches the ideal rate of inflation (zero) without becoming tangential to it — creating a natural value trend to which competing major currencies converge, as if acting in singularity.

The following charts represent how similarly the major currencies have related to bitcoin in a five year cycle:

£1 to bitcoin (source: Google)
€100 to bitcoin (source: Google)
$1,000 USD to bitcoin (source: Google)
¥10,000 to bitcoin (source: Google)

In all charts, the sovereign currency is approaching a 1:0 exchange rate with bitcoin, without achieving it, but only because bitcoin has an internal measurability and divisibility comparative to the sovereign issuance.

There is also another paradox involving bitcoin: if we take the supply of money as being ideally zero, bitcoin can’t be asymptotically ideal money since its issuance actually stops (circa 2140) and therefore becomes tangential to the rate it reaches toward.

Game Theory and Binding Agreements

By inverting the relationship (sovereign to bitcoin), the above charts show a price exchange pattern where bitcoin becomes the basis for asymptotically ideal money, without actually being that ideal itself.

As a medium of exchange with a steady and constant inflation representation, bitcoin offers a utility in something other than retail payments: if it is standard practice for contracts to adjust to inflation, why can’t contracts adjust to bitcoin inflation?

“A concept that we thought of later than at the time of developing our first ideas about Ideal Money is that of the importance of the comparative quality of the money used in an economic society to the possible precision, as an indicator of quality, of the contracts for performances of future contractual obligations.” John F Nash Jr., Ideal Money and Asymptotically Ideal Money (Relations to Law and Contracts), 2008

John Forbes Nash Jr.

The suggestion becomes self-evident that bitcoin is a realisation and extension of John Nash’s early works in non-cooperative games and bargaining: Nash introduced the distinction between cooperative games, in which binding agreements (contracts) can be made, and non-cooperative games, where binding agreements are not feasible, developing an equilibrium concept for non-cooperative games later known as Nash equilibrium.

The ideas of expectancy in bitcoin and Nash equilibrium also becomes clear: in a Nash equilibrium, all of the players’ expectations are fulfilled and their chosen strategies are optimal.

In this concept, Nash proposed two interpretations: one based on rationality (where information is common knowledge, for example, knowing how many bitcoins have been mined), the other on statistical interpretation (more applied in so-called evolutionary games of strategic interaction).

In later works, John Nash started considering pro-cooperative games.

By understanding the indexation in binding agreements (contracts), and the difficulty adjustment in bitcoin, a money need only be so good as to make good on its promise rather than hold value for all time: in 2015, Nash observed the difference between ideal money and the typical currencies would be somewhat intense, if not dramatic.

Ideas in games, language, and trust.