Different Evolutions of Ideal Money.
When Charles A. Holt wrote an article (John Nash: Flashes of Brilliance in Different Directions, Southern Economic Journal, 2015) about John Nash’s famous bargaining solution (1950) and its evolution into Nash’s subsequent Ideal Money, Holt observes to Nash he’s intrigued by the contrast between the precise mathematical result and the abstract nature of the assumptions. Nash smiles, and says he knew the answer before proving the theorem and then worked it backwards to deduce the nature of the product-of-differences solution.
When we compare this to Satoshi Nakamoto’s confession he wrote the Bitcoin code “backwards” because he first had to convince himself the code could solve every problem, there arises the similarity in methodology, further intensified by Bitcoin advocates regarding bitcoins as “ideal money” just as Nash described his bargaining assumptions as “idealizations” which equate to small amounts of money.
John Nash didn’t speak on Bitcoin to any great length, but one comment he made (in 2014, when addressing the Oxford Union) was comparing the bitcoins being minted in this well organised system (described as Caesar’s empire) to another Caesar who could then come along and introduce a “little lead” into the coins and pass them out at the same value.
The question here is if Bitcoin is an assumptive or axiomatic design — in the manner of Nash’s original bargaining solution — then can these assumptions or axioms be recreated in an aggregate which replicate the Bitcoin value proposition? The possibility further arises that some sort of digital sovereign issuance could then appreciate against a bitcoin in the way bitcoin has appreciated against traditional sovereign fiat currencies.
This idea has been with me for a year or two now, but it wasn’t until recently I found someone else thinking along these lines:
An Obvious Axiom
The way the cumulative bitcoin supply is programmed suggests a Pareto distribution, and this could be one explanation as to how bitcoin “long tails” against the sovereign fiats. This is demonstrable from any currency converter graph across a long enough time frame, and is something I’ve covered before (The Benefits of Cooperation: Nash Bargaining and Bitcoin, Bitcoin Magazine, 2024) in John Nash’s potential relationship to the Bitcoin design. One of the assumptions with a tail index is the greater value existing in the longer part of the tail rather than the initial head and body distribution, and would be one reason for explaining the pre-determined and fixed supply of bitcoins which escape the arbitrary inflation risks of centrally managed money (to paraphrase Satoshi).
The suggestion here is a new sovereign digital issuance > bitcoin > traditional sovereign fiats. Such a new sort of sovereign digital product may take the form of a growth bond. This would fall outside the remit of central banks if it’s issued to primary markets by Treasury’s. These bonds would have potential use in achieving public policy goals and lead even perhaps to the formation of multilateral currency coalitions if Bitcoin becomes a common and singular reference point of value: when it comes to cooperative game theory, there aren’t restrictions on how coalitions or agreements can be reached, and new evolutions or iterations of “ideal money” might direct the traditional bitcoin narratives to a different end-point of greater magnitude.
Different Evolutions of Ideal Money
The question of an “ideal money” has been around for some time before John Nash explicitly formalised his thoughts. Charles A. Conant (Is an Ideal Money Attainable?, Journal of Political Economy, 1903) wondered if a monetary standard could be better devised than gold or silver and which is more equitable than using coined money? Conant eventually answers his own question in the negative, realising heterogeneity of commodity preferences across time and space would make it difficult to reach consensus for the underlying basis of such a standard.
This is again where Nash and Satoshi converge: they both generalise the problem. Nash uses axioms to be satisfied in his bargaining solution, and Satoshi uses script so each transaction doesn’t require special support code and data fields covering one special case at a time.
Satoshi, in a message board post on 9th November 2008 to Hal Finney says he thinks he’ll be able to release his code sooner than write a detailed specification. Which raises a further question as to whether an “ideal money” system could further evolve by specification which satisfies some desirable assumptions? Initial work has already been instigated on this (see below correspondence).
