On the Curious Similarities Between John Nash’s Ideal Money and the Works of Nick Szabo

9 min readFeb 10, 2023

When I was first introduced to bitcoin, it was mostly through my revelations via a lecture and writing series called “Ideal Money”. When I went to find the bitcoin community to understand better what bitcoin was I came across Nick Szabo’s work.

I began to read both their work as fast as I could. Although it took years to be able to demonstrate I was absorbing it at all, I quickly begin to think, since at the time no one really knew who Nick Szabo was, that maybe Szabo was a pseudonym of Nash’s.

At the time I was already convinced Nash was Satoshi and couldn’t understand why others didn’t see what I saw. Here I would like to show some interesting connections between the three of these identities. And although its clear now that Nash isn’t Szabo, Szabo isn’t Nash, I think I can be forgiven for thinking that Szabo’s work is an extension of Ideal Money and that bitcoin is an implementation of it.

On Contracts and the Effects of Money on Their Formation

A smart contract is a computerized transaction protocol that executes the terms of a contract. The general objectives of smart contract design are to satisfy common contractual conditions (such as payment terms, liens, confidentiality, and even enforcement), minimize exceptions both malicious and accidental, and minimize the need for trusted intermediaries. Related economic goals include lowering fraud loss, arbitration and enforcement costs, and other transaction costs[1].~https://www.fon.hum.uva.nl/rob/Courses/InformationInSpeech/CDROM/Literature/LOTwinterschool2006/szabo.best.vwh.net/smart.contracts.html

Nick Szabo is often thought to be the creator of bitcoin and if you have traversed his works its not hard to see why. He was effectively building technology on bitcoin over a decade before it existed:

Digital cash protocols[2,3] are fine examples of smart contracts. They enable online payment while honoring the characteristics desired of paper cash: unforgeability, confidentiality, and divisibility. When we take a second glance at digital cash protocols, considering them in the wider context of smart contract design, we see that these protocols can be used to implement a wide variety of electronic bearer securities, not just cash.

For him it’s quite a natural extension to think about the evolution of contract law in relation to money as he not only holds a degree in computer science but is also a graduate of the George Washington University Law School.

Where I think Nash and Szabo synthesize is in regard to the quality of money and it’s relation to contracts:

…the question can be asked: “How do ‘good money’ and ‘bad money’ differ, if at all, for the valuable function of facilitating utility transfer?” But if we consider contracts having a relatively long time axis then the difference can be seen clearly.

Consider a society where the money in use is subject to a rapid and unpredictable rate of inflation, so that money worth 100 now might be worth from 50 to 10 by a year from now. Who would want to lend money for the term of a year?

In this context we can see how the “quality” of a money standard can strongly influence areas of the economy involving financing with longer-term credits.

More specifically Nash points out that a weak money standard perturbs contract formation and reliability:

Uncertainty perturbing the issue of the effective meaning of a contract is comparable to and analogous to a climate of lawlessness that would make contracts, in general, unreliable.

From another version:

…my basic point is simply that as the currency of the Sovereign tends to have less stability and less reliability of its value then the circumstances affecting the formation of business-relevant contracts become quite perturbed.

The reliability of the money medium standard in regard to contract law is a key part of Nick Szabo’s theory of money (and works in general):

The appraisal or value measurement problem is very broad. For humans it comes into play in any system of exchange — reciprocation of favors, barter, money, credit, employment, or purchase in a market. It is important in extortion, taxation, tribute, and the setting of judicial penalties. It is even important in reciprocal altruism in animals.

On Honest vs. Trusthworthy Money

Nick Szabo’s has a very relevant essay Trusted Third Parties are Security Holes in which it can be said at the very least Satoshi implemented a design for money that considered the exact security principle Szabo outline’s in his TTP paper:

While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model.

What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party.

Szabo extends and explains this concept with regard to bitcoin post-Genesis in his paper The dawn of trustworthy computing:

By its very design each computer checks each other’s work, and thus a block chain computer reliably and securely executes our instructions up to the security limits of block chain technology, which is known formally as anonymous and probabilistic Byzantine consensus (sometimes also called Nakamoto consensus). The most famous security limit is the much-discussed “51% attack”. We won’t discuss this limit the underlying technology further here, other than saying that the oft-used word “trustless” is exaggerated shorthand for the more accurate mouthful “trust-minimized”, which I will use here. “Trust” used in this context means the need to trust remote strangers, and thus be vulnerable to them.

I think this parallels well with Nash’s sentiments on what he refers to as ‘honest money’ and money born of honest and reliable policies. From the section entitled ‘Honesty is the Best Policy’:

But here is where I see the importance of honesty, as if like the honesty of a well-regarded classical European monarch or emperor. Sometimes the people in the USA have been told things like “inflation is not a problem” when statistics compiled by the Labor Department (following “classical” rules) indicate that there is, indeed, ongoing inflation.

If an appropriately honest government-like agency is to issue the actual currency, and to provide for the central bank deposits denominated in terms of that currency, for a money system, then it can also, naturally, compute the indexes that would measure the presence or absence of inflation or deflation.

On surface it seems quite tangential to Szabo pointing to the trustworthiness of the issuance of bitcoin but Nash really means to expose the same vector philosophically to his audience by means of this example:

If the Canadian money unit is “targeted” for 2% inflation and if it gains in value compared with the unit of the USA then this suggests that the actual recent inflation rate for the currency of the USA is at least 2%.

On the vector of the quality of a Money In the Nashian Versus the Szabonian Sense

I think many people haven’t spent much time thinking about bitgold and its relevance to bitcoin even though Satoshi cited bitcoin as being an implementation of it.

Bitgold had no finite supply and I think this would surprise people. Anyone could choose to mine as much bitgold as they wanted and this become one of the last problems to solve as Szabo explains about Hal Finney’s RPOW (which is itself ALSO an implementation of bitgold):

Hal Finney has implemented a variant of bit gold called RPOW (Reusable Proofs of Work). This relies on publishing the computer code for the “mint,” which runs on a remote tamper-evident computer. The purchaser of of bit gold can then use remote attestation, which Finney calls the transparent server technique, to verify that a particular number of cycles were actually performed.

The main problem with all these schemes is that proof of work schemes depend on computer architecture, not just an abstract mathematics based on an abstract “compute cycle.” (I wrote about this obscurely several years ago.) Thus, it might be possible to be a very low cost producer (by several orders of magnitude) and swamp the market with bit gold.

Szabo has a clever solution for this and I think that more attention should be called towards understanding it:

However, since bit gold is timestamped, the time created as well as the mathematical difficulty of the work can be automatically proven. From this, it can usually be inferred what the cost of producing during that time period was.

Simply put since bitgold required a server, a database, and timestamps for its solution and thus the creation of it can be separated into periods. If there is an agreeance that if twice the mining power mines twice the bitgold in a given period than the previous period, we might then say the bitgold units from the latter period are worth only half the amount of the otherwise equivalent units from the previous period (a little awkard to say but its the best can I think to explain I’m convinced this will be helpful for people to read. ).

Szabo describes this as happening through a market but I think really its best to just understand it through a lens of how we would agree to value the units from each period.

This way if a miner could produce bitgold units at a cheaper cost than other miners, and a cheaper cost than the market value they could sell them for, that miner wouldn’t be able to control the supply at their own will. They wouldn’t be printing units for cheaper than they could sell them for…they would be printing units at a lower cost and those units would be accordingly less valued by the market.

It is the difference between the former scenario and the latter with Szabo’s applied observation that I want to suggest parallels PERFECTLY with what Nash’s means to define as what would not be Ideal Money and what would be Ideal Money.

Again, it might seem quite orthogonal, because Nash’s approaches his subject from the inquiry into what might be the best basis for money if all of the major central banks were looking to have the same target. Nash uses the concept of pegging to gold as an example to draw out some of the ideal characteristics of a chosen peg as well as to illustrate some not ideal characteristics. Nash points out one of the aspects that could make a commodity an unfavorable choice or less than ideal is a dramatic change in the cost to mine it:

Nowadays, however, few would propose a return to the actual use of simply the metal gold as a standard, for the following reasons.(i) The cost of mining gold effectively does depend on the technology. Recent cyanide leaching techniques have made it possible again to profitability mind gold at formerly abandoned sites in the U.S. so that it is now a big producer. However, the unpredictability of the cost is a negative factor.

A dramatic change in the cost to produce the chosen peg would disturb the intended reliability and predictability of the issuance of the monies pegged to the underlying commodity. It means even if the peg held true there might all of a sudden be effectively infinite gold and therefore infinite central banked money units (although perfectly pegged to the infinitely supplied gold!)…

We can see that times could change, especially if a “miracle energy source” were found, and thus if a good ICPI is constructed, it should not be expected to be valid as initially defined for all eternity. It would instead be appropriate for it to be regularly readjusted depending on how the patterns of international trade would actually evolve.

Here, evidently, politicians in control of the authority behind standards could corrupt the continuity of a good standard, but depending on how things were fundamentally arranged, the probabilities of serious damage through political corruption might becomes as small as the probabilities that the values of the standard meter and kilogram will be corrupted through the actions of politicians.

This is where the Nashian and Szabonian Ideals for the quality of money coincide. They approach from different angles for different reasons but Szabo’s observation most certainly perfectly Idealizes bitgold by Nash’s definition from Ideal Money.

A Quote note on Asymptotically Ideal Money And Bitcoin

With bitgold viewed in regard to having periods we then have a simple generalized formula:

the total supply of bitgold = the sum of all periods of how much computing power mined versus the difficulty of the pow problem

Someone could come along with this and say “why not adjust the difficulty to the expected mining power that will mine the next period.” But of course we don’t know how much mining power will mine for future periods.

Yet this becomes a simple process control problem/solution and we can put into the formula for the ‘next period’s mining power’ the PREVIOUS period’s actual measured mining power (measured by the units produce with regard to the difficulty). That is to say we can ‘estimate’ the next periods mining power and then we can use the feedback from the ACTUAL mining power to re-adjust our ‘next estimate + error correction’.

We would then always be one period off of what Szabo and Nash are looking for in in the ideal quality of a money but over time we would be asymptotically approaching it nonetheless.

Thus I have suggested in my theory that Bitcoin quite literally and formally is an implementation of Nash’s Ideal Money.