An Inquiry Into John Nash’s Proposal For Ideal Money

This writing explores a special essay and lecture series by John Nash entitled Ideal Money. John Nash is already well known for redefining our understand of economics through various game theory related work. The Nash Equilibrium is one of the most widely cited solutions ever put forth yet Nash didn’t receive wide recognition for the significance of this contribution until nearly 40 years later. Our initial lack of understanding however did not deter Nash from continuing to provide many valuable solutions to incredibly difficult to solve problems while he waited for the rest of the world to realize the value of his insight. This essay argues that Nash’s proposal is on a level of significance far above his early work and is in fact the totality of the entire insight Nash had in the 60’s at the time he wrote his earliest groundbreaking work.

20 Years of Lectures and Writing on the Subject of Ideal Money

Ideal Money has many different versions of the argument Nash put forth almost none of which are well known to anyone including academic professors studied in the field of economics. Many of these versions can be found on Nash’s homepage hardly hidden among different folders that are available for public view. Each lecture or writing uses different metaphors and examples that use different economic events of our history or recent times to explain the concept of Ideal Money in different ways. One such paper was published in the Southern Economic Journal and this paper varies drastically with the other papers and lectures that are available. Nash presented the subject in a way that would be difficult to grasp with out the collective context of most or all the works.

The Origins of the Concept of Ideal Money

Nash said in an interview that the basic concept for Ideal Money came to him in the 60’s when he fled to Europe. His biography suggests that at this time he was having delusional episodes. One such “delusion” from this time had him running around suggesting that governments, communist and anti-communist alike, were colluding against the people and that he was going to be our “savior”. On the one hand such behavior would obviously be seen as extremely narcissistic and paranoid, on the other this writing will show not only did Nash never abandon this view but it was quite a logical observation to make. It also the conclusion of Ideal Money:

The Keynesian implicitly always have the argument that some good managers can do things of beneficial value, operating with the treasury and the central bank, and that it is not needed or appropriate for the citizenry or the “customers” of the currency supplied by the state to actually understand what the managers are managing, what exactly they are doing and how it will affect the “pocket book” circumstances of these “customers.”

I see this as analogous to how the “Bolshevik communists” were claiming to provide something much better than the “bourgeois democracy” that they could not deny existed in some other counties. But in the end the “dictatorship of the proletariat” seemed to become rather exposed as simply the dictatorship of the regime. So there may be an analogy to this as regards those called “the Keynesians” in that while they have claimed to be operating for high and noble objectives of general welfare what is clearly true is that they have made it easier for governments to “print money”.

So I see the Keynesians as in a weak sense comparable to the “Bolsheviks” because of the support of both parties for a certain “lack of transparency” relating to the function of government as seen by the citizenry.

How Can We Define (A Stable) Metric For Value

Understanding value is not easy which is really a symptom of not having a stable metric for it. This is something we can begin to understand by thinking about how we evaluate money and commodities on markets that give us price signals for them. Put another way we might ask how we can objectively evaluate government issued fiat of any given nation. If, for example, we are to compare the Euro to the US dollar we might observe at some period of time that the exchange rate for Euro is falling. This might be an indication in a loss of value, however, if the price of the Euro is rising in relation to the Venezuelan Bolivar this might suggest not that the Euro is necessarily losing value but that both the US dollar and the Euro are increasing in value and that the US dollar is simply increasing more or faster than the Euro.

Because each of the currencies have floating exchange rates in comparison to each other, and each central bank that issues these currencies has their own policy and control over inflation, no currency really functions as a long term stable comparison for value.

However, if we measure a given currency versus a basket of currency prices this would be a more objective valuation than the comparison to just one currency. This is a comparable observation to how central banks measure and target inflation:

…its was the observation of a new “line”…for “central banking” functions relating to national currencies that gave us the idea for the study of “asymptotically ideal” money.

The idea seems paradoxical, but by speaking of “inflation targeting” these responsible official are effectively CONFESSING…that it is indeed after all possible to control inflation by controlling the supply of money (as if by limiting the amount of individual “prints” that could be made of a work of art being produced as “prints).

How would they do this? The means for measuring inflation that they would naturally use would be a “cost of living” index relation to domestic prices within the territory of the state.

On a domestic level an aggregate of different prices helps provide a reasonably objective measure for comparing the inflation of a respective money. The argument Nash paints is based around a comparable concept he calls an ICPI. The ICPI would be an optimally chosen basket of international prices which would provide an international basis for value comparison.

Isn’t Gold Stable In Value?

Historically at times gold has provided a reasonably stable basis for value although it is said we were never truly on a gold standard. At the end of WWII much of the world moved on to a de facto gold standard in which the US pegged their currency to gold in what is known as the Bretton Woods Agreement. This standard lasted until the 70’s when the US abruptly abandoned the standard and the world was forced to follow suit and move to the floating exchange system we have today

Some economic philosophers suggest we strive to achieve such a gold standard, however, as noted in Ideal Money this might not be optimal:

Nowadays, however, few would propose a return to the actual use of simply the metal gold as a standard, for the following reasons:

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.

The location of potential gold-mining locations may not be “politically appealing.” so it would seem undesirable to make a political choice to enhance the economic importance of those particular areas.

There is some negative psychology about gold such that even if it were the most logical choice after all, the unpopularity of the idea could be very obstructive.

Nonetheless one would expect gold to be a component of Nash’s ICPI

The Misrepresentation of Nash’s Theoretical ICPI

The ultimately launched concept of “ideal Money” become possible when I conceived of a practical basis of a standardization of the comparison of the value of the currency with an appropriate standard of ideal.

Not many people have been exposed to the bulk of Nash’s argument and often people mistakenly believe that Nash suggested we should peg our money to a politically constructed ICPI. Although the ICPI is the basis for the special insight it is not itself a solution as Nash’s points out because it would be need to be adjusted over time which introduces the possibility for political pressure:

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.

However, pegging money to an ICPI was NOT Nash’s proposal:

It seems possible and not unlikely, however, that if two states evolve towards having currencies of more stable value as measured locally by national CPI indices that then also these distinct currencies would tend to evolve towards more stable comparative relations of value.

Then the limiting or “asymptotic” result of such an evolutionary trend would be in effect “ideal money” but this as a result achieved without the adoption of anything like an ICPI index as a basis for the standard of value.

Understanding the Purpose of Defining a Theoretical ICPI

Nash’s ground breaking solutions and papers are well known for having a very special flare. He solves problems from angles his peers admit they would never have thought to think from and his solutions often have what initially seems to be leaps of logic. Often years later when we fully understand his work we can work through the logic to see that it's all there but rather it was just so paradigm shifting it seemed like there could be no bridging explanation.

Ideal Money works like this. It is basically mathematical induction. It’s like building a form for a bridge and then once the final keystones are in place the bridge holds on its own no longer needing the form.

Nash’s argument in a nutshell is that, although, we cannot design a money that is perfectly stable in value, we could see that money that does approach stable value can necessarily be said to approach a limit that WOULD BE comparable to an optimally chosen basket of commodity prices.

This observation in itself might not seems like a special or valuable insight, but it is what set Nash over the edge when the idea come to him. It’s also his life’s work and something he spent the last 20 years of his life giving lectures on.

What is the Significance of Nash’s Insight?

The ultimately launched concept of “Ideal Money” became possible when I conceived of a practical basis for a standardization of the comparison of the value of the currency with an appropriate standard ideal.

The significance of this idea is what you can extrapolate from it-not the idea itself. From this viewpoint of observing that if money were put on a stage of competition in which it must compete to survive we can begin to ask what is needed to create this phenomenon.

The below is a lengthy and wordy paragraph but incredibly revealing and further shows the genius of John Nash’s proposal:

I think there is a good analogy to mathematical theories like, for example, “class field theory”. In mathematics a set of axioms can be taken as a foundation and then an area for theoretical study is brought into being. For example, if one set of axioms is specified and accepted we have the theory of rings while if another set of axioms is the foundation we have the theory of Moufang loops.

So, from a critical point of view, the theory of macro-economics of the Keynesians is like the theory of plane geometry without the axiom of Euclid that was classically called the “parallel postulate”. (It is an interesting fact in the history of science that there was a time, before the nineteenth century, when mathematicians were speculating that this axiom or postulate was not necessary, that it should be derivable from the others.)

So I feel that the macroeconomics of the Keynesians is comparable to a scientific study of a mathematical area which is carried out with an insufficient set of axioms. And the result is analogous to the situation in plane geometry, the plane does not need to be really flat and the area within a circle can expand hyperbolically as a function of the radius rather than merely with the square of the radius. (This picture suggests the pattern of inflation that can result in a country, over extended time periods, when there is continually a certain amount of gradual inflation.)

The special axiom is again not necessarily novel until we begin to flip the perspective. Nash highlights it here:

The missing axiom is simply an accepted axiom that the money being put into circulation by the central authorities should be so handled as to maintain, over long terms of time, a stable value.

The Problem With Central Banking

Central banks aren’t evil. Most people that suggest banks are immoral don’t understand the purpose of central banking. Central banks adjust the money supply via inflation rate policies in order to reflect economic growth (or decline of growth). Central banks usually favor slight inflation, however, this attitude can change depending on political and economic circumstances.

Stability of value is the general goal but a predictable rate is sometimes favored over perfect instability in order to serve exports and imports needs. If the value of a currency begins to rise especially in relation to other relevant currencies then export number suffer. If exports are expected to fall and the economy will suffer central banks will often devalue their currency in order to make exports cheaper for foreign buyers.

The contrasting views between the search for an internationally stable metric of value and the want to increase inflation to spur economic growth somewhat highlights what is known as the triffin dilemma:

The Triffin dilemma or Triffin paradox is the conflict of economic interests that arises between short-term domestic and long-term international objectives for countries whose currencies serve as global reserve currencies.

The currencies in the world don’t really compete in a way that makes them strong over time, rather, different respective nations are sometimes and often in a race to devalue. In contrast devaluing a reserve currency (such as the US dollar is sometimes said to be) has its own ramifications. So there is pressure both ways to not seek stability of value even if in the long run it would be optimal for all nations and their respective citizens.

The Importance of a Stable Metric For Value

We tend to think of currency as a medium of exchange for value. But this function can be viewed a side product of our want for effective value comparison. When the value changes, however, money no longer serves this purpose.

Nash explains the importance of a stable unit of value with this example:

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

From a short term individual view the the importance of money seems to be to serve everyday transactions but the real problem we face as a global economy is how to get onto the same incorruptible value standard.

Bitcoin as the Premise of Nash’s Proposal

From the perspective of Nash’s insight we can extrapolate every aspect of bitcoin as a catalyst for the evolution of our money systems towards what would be comparable in stability to an optimally chosen basket of commodity prices (ICPI). What is needed is the introduction of an internationally traded currency or commodity that is as good or better than other alternatives available. This is exactly what Nash calls for:

I think of the possibility that a good sort of international currency might evolve before the time when an official establishment might occur.

Here I am thinking of a politically neutral form of a technological utility.

To be quite respectable, in a Gresham-advised sense, money needs only to be AS GOOD as other material commodities that might be hoarded.

Bitcoin is slowly becoming understood to function as a form of value storage for much of the same reason that gold has historically played this role. Not necessarily the scarcity of supply but the relation of the supply to the cost of mining which bitcoin effectively mimics. Bitcoin provides a fairly stable (but not perfect!) and predictable measure of value which the markets can rely on as an inflation hedge. Nash even perfectly predicts bitcoin’s inflation schedule which decreases by half every 4 years:

Now the possible area for evolution is that if, say, an inflation rate of between 1% and 3% is now considered desirable and appropriate in Sweden, then, if it is really controllable, why shouldn’t a rate between 1/2 % and 3/2 % be even more desirable?

As bitcoin becomes more relevant and traded for more currencies across more exchanges central banks will find themselves competing with bitcoin for relevance. As customers of fiat the citizens will naturally put pressure on central banks to print money of a higher quality in regard to stability of value just as Nash predicted 20 years ago:

The currencies being compared, like now the euro, the dollar, the yen, the pound, the swiss franc, the swedish kronor, etc. can be viewed with critical eyes by their users and by those who maybe have the option of whether or not or how to use one of them. This can lead to pressure for good quality and consequently for a lessened rate of inflationary depreciation in value.

The ultimate result of this phenomenon is that our money systems will hit the ceiling of ideal-ness that Nash describes as being comparable to an ICPI (again without ever implementing an ICPI). This allows us to return to his original claim that otherwise competing governments and their respective central banks effectively collude against the people's best interests. Nash’s claim that he would solve this problem is actually rational:

…this standard, as a basis for the standardization of the value of the international money unit, would remove the political roles of the “grand pardoner's,”…

This insight is what causes Nash to declare:

…a process of political evolution might lead to the expectation on the part of citizens in the “great democracies” that they should be better situated to be able to understand whatever will be the monetary policies which, indeed, are typically of great importance to citizens who may have alternative options for where to place their “savings”.

On The Difficulty of Traversing Nash’s Argument

Much of Nash’s work is difficult to understand. He is well known for unapologetically putting forth solutions with seemingly little explanation. Ideal Money however was an insight Nash felt would not go over particularly well with those that traditionally held the monopoly on money printing:

The script or plan for my talk linking the “ideal money” with the choices and actions of “thrift” or “savings” by persons or by “economic agents” was influenced by concerns that it would be wise not to speak too incautionsly of “the Keynesians” when the times are such that massive public opinions maybe supporting actions by which a state administration can act without going through the parliamentary processes to write new legislation.

So in the rush of political campaigns and elections (for example in the USA) it is difficult to sell a national monetary policy which, if followed consistently on a “long run” level, would result in the specific nation state existing as if on a higher level of economic civilization.

(For example, Sweden and Argentina might be usable, over a long time comparison, to represent comparable “economic civilizations”.)

Therefore, I had arranged for 2012 to talk more cautiously in relation to whatever would impact with “the Keynesians” and with the political interest relating also to the scholarly factions allied with (or forming) “the Keynesians”.

And this caution carries over naturally to 2013 also.

I am speaking about a research project that is not fully complete since I have not yet written up and submitted for publication any paper or papers describing the work. Also the details of what axioms to use and how to select the basic set theory underlying the hierarchical extension to be constructed are not fully crystallized. I have also a great fear of possible error in studying topics in this area. It is not rare, historically, for systems to be proposed that are either inconsistent or that have unexpected weaknesses. So I feel that I must be cautious and proceed without rushing to a goal. And this psychology of fear has also inhibited me from consulting other persons expert in logic before I could feel that I had gotten my own ideas into good shape.


The conclusion has already basically been expounded on but there is a relevant point to be made in regard to bitcoin. The community of early bitcoin adopters is said to be in a civil war with itself. On the one hand there is a faction of people that are basically ignorant to the concept of central banking practices and their purpose who are arguing for “hyperbitcoinization” which is the idea that bitcoin will eventually usurp all central banks and cause hyperinflation of all fiat.

This is simply the conclusion of someone that doesn’t properly view the role of central banks:

The idea seems paradoxical, but by speaking of “inflation targeting” these responsible official are effectively CONFESSING…that it is indeed after all possible to control inflation by controlling the supply of money (as if by limiting the amount of individual “prints” that could be made of a work of art being produced as “prints).

The proper outlook for bitcoin when we consider how central banks actually work is for it to be a catalyst that improves central banking practices and the quality of money central banks issue in regard to stability of value. This is explained in a congressional research report on bitcoin:

Regarding the velocity of money, if the increase in the use of Bitcoin leads to a decrease in need for holding dollars, it would increase the dollar’s velocity of circulation and tend to increase the money supply associated with any given amount of base money (currency in circulation plus bank reserves held with the Fed).

In this case, for the Fed to maintain the same degree of monetary accommodation, it would need to undertake a compensating tightening of monetary policy.

What has happened is Nash has given the proper logical and founded argument for the optimal use-case for bitcoin. While many people new to bitcoin and uneducated in economics are rallying behind a movement to scale bitcoin to be an everyday coffee money that anyone in the world can use for a low fee bitcoin is slowly showing itself to be resilient towards this movement and instead is slowly starting to be heralded for its gold like qualities as an inflation hedge.

At the same time actual experts in the field are noting that bitcoin can’t necessarily scale to serve the entire population of the world so soon in its infancy. As a matter of fact that the transaction capacity cannot scale on the base layer may in fact lend to the predictable nature of bitcoin’s value proposition further solidifying its role as a new digital gold.

As bitcoin’s fees rise the average user that doesn’t understand the macro-economic implications of bitcoin starts to get frustrated. But as the currency’s inflation rate continues to decline bitcoin will eventually be effectively scarcer in supply than gold. As the network effect continues to drive the price the fees increase. This cannot be seen as a fatal flaw since the high fees are in fact an indicator that there is such a demand for the limited transaction space. As this demand for a stable store of wealth increases the price of bitcoin in respective fiat money increases which allows higher and higher value players to enter the market. Eventually we should expect large hedge funds and even central banks to hold substantial positions in bitcoin.

At this point bitcoin as a settlement system will serve as the perfect catalyst John Nash described that will “asymptotically” take the power from central banks to arbitrarily print money against the ultimate good of the people.

It’s been suggested Nash might be the mastermind behind bitcoin, but whether he had something to do with the project or not does not take away from the specialness of the proposal Ideal Money. Nash’s Ideal Money is clearly premised on bitcoin, whether he knew about it or not, and more importantly Nash left us the logical founded argument for how bitcoin should be scaled well before the technology existed.

As more and more academic and economic professors learn about bitcoin and Nash’s argument a new revolution of people will lend support to this theory. At this point bitcoin nature as a digital gold will be preserved by knowledge economic experts and professors around the world. Nash’s proposal will be the foundation for such a movement.