Meditations on a Formal Model for The Problem and Solution to our Global Economy

19 min readJul 17, 2018

I have always had a certain intuition I couldn’t properly express with regard to John Nash’s Ideal Money and it’s impending relationship to Bitcoin. The basic point is that central banks will already be caught subscribing to an Ideal system (basically an apolitical value standard) well before the public (or academia for example) demands it. Why and how this might be so is a little more difficult to understand.

I recently re-read a paper created for my country’s central bank by Warren E. Webber called A Bitcoin Standard: Lessons from the Gold Standard. I found a formula in it that I have longed for.

It is the formulated observation that a globally used medium of exchange inspires exchange rate stability between major currencies AS the cost to arbitrage with the medium tends towards zero cost. The author of the paper I mention makes two observations on the nature of arbitrage in relation to monetary policy:

…the monetary authority in Country A cannot set its bank rate too high. Otherwise, the resulting gold inflow will offset what they were attempting to achieve by raising the bank rate.

… the monetary authority in Country A cannot set its bank rate too low. Otherwise, the resulting gold outflow will offset what they were attempting to achieve by lowering the bank rate.

Putting these together we have the formalization:

Which effectively shows:

…the cost of gold arbitrage in effect determined a policy corridor in which a central bank could set its bank rate different from other bank rates.

What the formula further suggests is, as the cost of using gold to arbitrage limits to zero, the “policy corridor” also limits to zero:

Under a Bitcoin standard, however, it will not be possible for a country to conduct an interest rate policy to affect domestic economic conditions. As (1) shows, it was the cost of engaging in gold arbitrage that allowed a country to set a bank rate that differed from those in other countries under the gold standard. Such arbitrage costs do not exist for the Bitcoin standard; that is, k = 0. The costs of arbitrage between the fiduciary currencies of any two central banks are essentially zero. The time cost of obtaining Bitcoin for fiduciary currency or fiduciary currency for Bitcoin would be extremely small, and because the ledger containing transactions history is open and transactions are recorded regardless of location, no shipping or insurance costs are involved. Thus, the spot exchange rates for all fiduciary currencies would be one-to-one, and monetary authorities would be unable to set interest rates different from those in other countries.

Re-Visiting Szabo on Metcalfe’s Law

This observation reminds me of Nick Szabo’s insight in the essay Transportation, divergence, and the industrial revolution. Szabo shows,in an equally distributed economic network, a reduction in “transportation costs has a dramatic effect on the efficiency gained from the reduction:

Metcalfe’s Law states that a value of a network is proportional to the square of the number of its nodes. In an area where good soils, mines, and forests are randomly distributed, the number of nodes valuable to an industrial economy is proportional to the area encompassed. The number of such nodes that can be economically accessed is an inverse square of the cost per mile of transportation. Combine this with Metcalfe’s Law and we reach a dramatic but solid mathematical conclusion: the potential value of a land transportation network is the inverse fourth power of the cost of that transportation. A reduction in transportation costs in a trade network by a factor of two increases the potential value of that network by a factor of sixteen. While a power of exactly 4.0 will usually be too high, due to redundancies, this does show how the cost of transportation can have a radical nonlinear impact on the value of the trade networks it enables. This formalizes Adam Smith’s observations: the division of labor (and thus value of an economy) increases with the extent of the market, and the extent of the market is heavily influenced by transportation costs (as he extensively discussed in his Wealth of Nations).

It is an interesting evolution of the usefulness of Metcalfe’s law. One could argue that Metcalfe’s law, that the value of a network is proportional to the users/nodes, doesn’t take into account that some users won’t be as valued or as valuable as others. For instance, if everyone in the world plugs fax machines in but doesn’t use them does the fax network increase by the N factor Metcalfe predicts?

Szabo seems to allude to this limitation by the use of the word “potential”.

But in thinking of a banking system, specifically arbitrage between major financial institutions of the world, there isn’t such a redundancy since the whole point would be that all participant have something to gain by adopting the new medium (this is different than the game theoretical question as to whether or not each individual “player” or nation etc. could realize a unilateral gain since cooperatively achieved utility CAN be also considered).

On The Value of a Single Apolitical Monetary Standard

The central bank paper cited earlier does see that there would be significant value to having the world function on a Bitcoin standard:

A Bitcoin standard would have two major benefits over current fiat money standards. One is that there would be greater price-level predictability due to the known, deterministic rate at which new Bitcoins are created. A second is that the resources currently devoted to hedging against fluctuations in exchange rates would be freed up to be used in more productive ways.

John Nash also felt such a scenario of a single apolitical value standard would be “tremendously” valuable:

…a global money standard could have a value similar to that of standard measures such as those of the metric system.

There is tremendous value in simply having prices quoted conveniently.

Diverging Opinions On Game Theory and Political Implications

Here is where the paper differs from Nash’s opinion however:

Nonetheless, in my opinion it is unlikely that the Bitcoin standard will come into existence, because governments and central banks will take actions to prevent it.

I think it’s quite interesting that we might tolerate a paper that admits that a Bitcoin standard would increase the productivity of our global economy and yet there could be a counter-argument (in the same paper) that our elected representatives might have the power and will to suppress the advance to such a higher level “technological” advancement.

I am not at all convinced that governments have a say that is separate than the population that elects them. But this contention is not perfectly palatable for people especially those with anarchic, skeptic, or conspiratorial beliefs about how governments operate (or perhaps even those such as Edward Snowden who KNOW how governments operate in regard to nefarious anti-constitutional behavior).

As we can see John Nash quite explicitly believed we WOULD tend towards a single standard and that the political implications do not prevent such a change:

Thus I think that “asymptotically ideal money” is a real possibility and that problems of political coordination do not make this very difficult to be achieved. But also, if there is in the first stage of progress the advent of “asymptotically ideal” currencies then after that level of what might be called “rationalization” is achieved there would be the possibility of an international collaboration to set up value standards analogous to the standard measures used in the internationally accepted “metric system”.

We can note how perfectly relevant his argument is (but 20+ years later!) and how he still speaks to a future time we have not yet quite arrived at.

Furthermore, the central bank paper talks about the possibility of different equilibriums being possible in regard to the introduction of Bitcoin as a savings option. But the paper does not use the formal term for equilibrium which is “Nash equilibrium”. This is an important omission because it hides the fact that the author is actually relying on Nash’s game theoretical work that earned him a nobel prize (40 years after publishing!) while explicitly disagreeing with the game theoretical observation Nash makes in regard to the introduction of an international ecurrency with a stable supply:

The actors on the stage of the drama formed by the actions that determine the trends in the value of a national currency are themselves players in a game and they can be rationally viewed as such. The theme of “rational expectations” naturally enters. Those who ARE NOT in control but who ARE naturally concerned with the expectations for the value trend of a national currency cannot be wisely assumed to be entirely naive and unable to form “rational expectations” regarding the currency. So the (possibly) “Keynesian” players in this game have natural opponents (or co-players, beyond zero-sum perspectives) who are interested in not being themselves “outsmarted” by those who control the options that determine, say, the quantity supplied of the national currency.

The author of the paper, Weber, has to either admit he missed this game theoretically based reasoning, or that he is in disagreement with the person that is responsible for the work he is citing.

To be clear and to summarize Nash said he believes you can rationally view it game theoretically and the political coordination difficulties therefore do not pose a problem to achieve a single internationally held monetary standard.

On the Significance and Pursuit of a Stable Money

This paragraph, in which the author introduces the possibility of a euro type currency backed by a basket of commodities, is very telling of their understanding of money in my opinion:

Another possibility is there could be political pressure demanding that central banks or governments offer an intrinsically useful fiduciary currency to compete with Bitcoin. By an intrinsically useful fiduciary currency I mean a currency backed by some commodity or basket of commodities. If central banks or governments could credibly commit to redeem this currency on demand, and if they were willing to give up their own monetary units and adopt a uniform one, then this might be widely accepted as a medium of exchange and might drive out Bitcoin to a great extent. My reason for including the elimination of individual country monetary units is to make clearing simpler and to facilitate the use of the currency across country lines. In other words, the Bitcoin standard might not be stable because a eurolike commodity-backed money could provide the benefits of the Bitcoin standard without its inherent stability issues.

It is often believed we are in a pursuit of stable money (even though we can’t have a measure for what money is stable). It is difficult to believe that a money that was secularly deflationary wouldn’t be favored, if given the choice, over a money that is “stable” comparatively (however we might define stable).

Stable money isn’t what is desired I think. Savers want a non-inflationary option, certainly, but would rather deflationary than stable no doubt.

Money that doesn’t fluctuate wildly would be preferable than money that does, and in this sense “stability” is favored. If it can be said a money can be deflationary and stable in the latter sense then I agree stable money is preferable.

However to think that a money pegged to a basket of commodities, redeemable for such, would outperform a money that has a trustworthy issuance based on an unchangeable algorithm that regulates the supply in relation to increased pressure I think is to not understand the purpose of inflation targeting.

Some people feel that inflation targeting, such as keeping a locally observed basket of prices stable by use of monetary policy tools, keeps the purchasing power of the respective currency stable to the target % desired. Lars Christensen gives a different explanation for the role and purpose of inflation targeting:

What he explains is that inflation targeting is a type of promise to the users of the currency. It is less a guarantee of purchasing power by means of currency supply manipulation and more of rule set that the users base can use to predict the quality of the currency (whereas the outcome or indirect result is supposed to be also a money with a stable purchasing power).

This is better understood as we understand that you can manipulate the composition of the basket of prices being used such that there is more or less inflation observed than if a different set of prices were used. And this trend could vary widely with a more internationally observed orientation (ie in relation to other currencies or world commodity prices). So one Venezuelan political party might observe X% inflation while another observes Y% each depending on the composition of the basket of prices used for analysis while the rest of the world sees Z% from an external view.

To suggest that a euro type currency could emerge, regardless if it was “backed” by actual commodities that could be redeemed for, is to suggest that such backing would be more trustworthy than Bitcoin’s “rules”.

The simple point is that there is a ceiling on quality here; you can’t be more trustworthy than trustworthy.

On Applying Game Theory

When John Nash proposed his Nash Equilibrium theory he suggested poker would be an obvious target for its use. Years later most pro’s have learned of the existence of Nash Equilibriums. Especially with tournament players it is not uncommon to frequently use phrases such as “I would go with Nash here”.

Here we consider Wil Tipton’s observations on the proper use of the Nash Equilibrium in regard to games:

GTO play is in some sense “correct”. For example, in the game of rock-paper-scissors, the GTO strategy is to throw each choice randomly 1/ 3 of the time. Of course, it is hard for humans to be completely random, but insofar as you can, nobody will be able to beat you in RPS in the long term if you play this strategy. However, if you are ever playing a strategy that involves throwing any action with other than a 1/ 3 probability, your opponent can take advantage of you. In fact, he can do very well just by figuring out your most likely throw and using whatever counters it 100% of the time, at least until you notice and change your strategy.

This motivates the primary reason we will focus on GTO play. You have to have some idea of what it looks like before you can even start thinking about what your opponent is doing wrong and implementing a strategy to take advantage of it. You must know that the correct rock-throwing frequency is somewhere around 1/ 3, before you are able to come to the conclusion that an opponent who throws rock 40% is doing it “too much”. Once you know what your opponent is doing and how that deviates from correct play, it is pretty easy to see how to exploit it. The same thing is often the case, to a degree, in poker. Once you know what “correct” play is and can compare it to an opponent’s strategy, figuring out an appropriate response is usually not all that difficult. The difference between RPS and poker, however, is that poker is much more complicated. In fact, nobody really knows what this correct play is.~Tipton, Will. Expert Heads Up No Limit Hold’em, Volume1: Optimal and Exploitative Strategie

Noting specifically the bold most players miss this proper orientation using the Nash Equilibrium. A basic corollary of the NE is that as the playing field limits towards perfect play it is more important to also play towards the Nash Equilibrium, however, if the opponents are not perfect then we would want to deviate from the Nash equilibrium and use it to find the counter strategy that gives us the highest pay.

Most intermediate players move straight to the latter, because they know the average tendencies of weaker players, while the top pros spend their time trying to discover the perfect balance points in situations because it teaches them when and how to adjust most properly (and that intermediate players don’t spend any time considering the Nash Equilibrium strategy which limits their ability to play in champion level games).

Perhaps this differing psychology might change if the the game is ever truly “solved”.

Approaching Optimum From a Cosmological Perspective

It might seem like tangential leap to begin to consider to the relationship of the problem of our global economy to a cosmological consideration. But I think what is more likely is that our limited understanding of our economy limits our understanding of the nature of “currency” and its relation to the cosmos.

Thinking game theoretically it would be most beneficial if we knew what was optimal (from a game theoretical sense) as it would allow us to extrapolate proper strategies (and counter strategies!) to move towards it.

Here I think the problem of our monetary system, if we consider that a Bitcoin standard might be a higher paying equilibrium, becomes comparable to the problem of bodies trying to find an orbital or relational equilibrium.

The simplest case would seem to be the relationship between two bodies which might be too simple in comparison to three bodies. We might render the model more comparable to the problem of our global economy if we imagine the bodies being planets with populations that ultimately “vote” on the orbital relationship of the bodies (perhaps at some infinitesimal level this happen via states of micro-particles).

Then a two bodied relationship is a matter of which body is subservient and from a local perspective their wouldn’t be much difference regardless.

But with three bodies two bodies have to agree to be subservient and so I think the political complexity intensifies.

This would be simpler again if for example one of the three bodies was a sun.

From this perspective the complexity of organizing all the currencies without a “sun” seems obviously complex to the degree it is unsolvable for us (we haven’t yet generalized a 3 body solution as I understand).

Re-visiting the Political Divisions of Red Versus Blue

Pick a side, the colour doesn’t matter. You are your side with your beliefs based on your experience. The other side, red if you are blue, is the person or people in the world that have views so counter to yours it’s unfathomable to you how they could be so ignorant.

And they feel perfectly the same about you.

In a recent article I talked about a construct which divided the world “politically” into red versus blue. There was specific purpose for why I evoked it but here it a simplification of politically diverse views. For any controversial decision you are going to a certain threshold of the population in order to counter change. For non controversial issues change either happens or doesn’t and there is no division created. But here we are pointing to issues that are controversial to the point that there is an equilibrium created in which unwillingness to change is perfectly matched with want for change.

The basic point here is that, politically, complex arrangements of differing beliefs end up either being insignificant or end up getting generalized into opposing beliefs creating a “heads up” type division. From another view it is as if the only possibilities are stability versus change or increased simplicity of political orientations which leads to change.

In this sense, simplicity helps bring about a higher pay-off. This is conducive with Nash’s observations that the introduction of a currency can render the game such that it is not zero sum for the participants that previously faced only zero sum decisions:

(1): Games with transferable utility. (and) (2): Games without transferable utility (or “NTU” games). In the world of practical realities it is money which typically causes the existence of a game of type (1) rather than of type (2); money is the “lubrication” which enables the efficient “transfer of utility”. And generally if games can be transformed from type (2) to type (1) there is a gain, on average, to all the players in terms of whatever might be expected to be the outcome.

This is not a new, or unaccepted insight, and was actually captured and formalized by Nash in The Bargaining Problem around the same time his equilibrium paper was written. He revisits the thesis later in his Ideal Money meditations:

Here we can return to the understanding that money has the practical value of creating games for traders. These are games with transferable utility, but if the money were not available, the game of the traders would be a game without transferable utility and thus naturally a game with less efficiency with regards to the possibilities for the participants to maximize their combined gains.~Ideal Money

On The Heliocentric Perspective

It is often argued that observable reality is enough to convince a rational person to change their inconsistent view. I don’t mean to argue that any perspective is perfectly acceptable (as Feynman lectures some models allow us to make more accurate predictions than others) but we can note that a geocentric model of our cosmos served to help our population scale to the point we are at now. So it was viewed empirically as being useful at the time.

It is interesting after all that change we still sort of mock ancient civilizations for their religious based worship of the sun as if it was a god.

Nonetheless in regard to political alignment it might be seen as impossible to simply use observations on reality in order to properly align complexly fragmented views since different models might work for “all intents and purposes”.

On Stable Crypto-Currencies

Not long ago I was passed a working paper on a “stable-coin” algorithm. Since it is computer scientists that now have control over the evolution of our money there is some observable misconception in regard to what we are searching for and what the remaining problems are that are useful to be solved. Satoshi couldn’t have created Bitcoin to be stable in purchasing power. That was one of the problems that couldn’t be solved. What Satoshi necessarily realized is that you can’t create an elastically supplied money such that it creates a stable purchasing power simply because there is no such measurement for stable purchasing power to base algorithmic adjustments on.

Satoshi’s great advance came with the simple realization that a finitely supplied money might not be optimal in the elastic sense, but it would still be favored as a hoardable medium like gold. He solved the problem of implementing a workable apolitical ecurrency by removing the attempt to solve the problem of a currency with an optimally elastic supply.

What the paper I was sent proposes is nothing really novel. When you have a trustworthy exchange price (ie an oracle) you can easily programmatically stabilize a currency to it (provided such a currency has reasonable relevance etc).

So while the author was trying to create a money with an actually stable purchasing power the generalized formulas they give are unworkable EXCEPT if they use something like the price of Bitcoin as an oracle.

For a decentralized optimally elastic apolitical currency this doesn’t make sense. If you are value stable with Bitcoin why are you better than Bitcoin? If you aren’t using Bitcoin as the oracle then what apolitical price do you have access to?

The paper used a secondary medium as a sort of counter weight and market/arbitrage process which would keep the units of the stable-coin in proper ratio with the intended target. That the competition between those that “bet” for or against the stability of the coin creates stability I think is another comparable observation of an equilibrium between red and blue.

After I read the paper I suggested to the author that they consider their paper as a proper for the algorithm that the sub-economies of the world might use to stabilize the issuance of their currency with Bitcoin.

In other words if governments and central banks decide to move to a Bitcoin standard it will be via a similar algorithm and so I the formula from the central bank paper and the algorithm I allude to here help suggest the formalization of a game theoretically optimal solution to a simple but sufficiently complex enough model of our global economy.

On the Comparability of a Bitcoin Standard and Bitcoin as an Inflation Target

I’ve suggested to many economic professors, academics, and central bank researchers that the exchange price for Bitcoin provides the perfect basis for John Nash’s argument. Nash argues the world would be on an ideal standard if all the major currencies were in perfect stability with an apolitical price. His example was a basket of world currencies he calls an ICPI (Industrial Consumption Price Index) but he noted that doesn’t remove the political problem since some external entity would need to readjust the basket over time as different commodities become (perhaps wildly) more or less relevant.

Out of the replies I do get they often misconstrue my suggestion to mean some sort of a Bitcoin backed issuance of money. It’s too much of a stretch to suggest that the same role and function of a central bank could remain but simply that the inflation target move from observations on local price trends to the observations of the change in exchange price of the domestic currency for Bitcoin.

What is quite clear to me, especially after reading that bank paper, is that each scenario is effectively the same thing. Since they both imply perfect exchange stability between bitcoin and the centrally banked currencies (and inter-relationally between those different currencies).

On Rationalization

I previously stated or implied in a debate that Nash suggested there would be a period of “rationalization” where central bankers and related authorities begin to understand the insight expressed in Ideal Money. That they will become more rational en masse as the problem and solution of our global economy become clearer.

This would be in line with this definition:

Rationalization is a reorganization of a company in order to increase its efficiency. This reorganization may lead to an expansion or reduction in company size, a change of policy, or an alteration of strategy pertaining to particular products.~

I subsequently came across this definition of the word from the psychology field:

In psychology and logic, rationalization or rationalisation (also known as making excuses[1]) is a defense mechanism in which controversial behaviors or feelings are justified and explained in a seemingly rational or logical manner to avoid the true explanation, and are made consciously tolerable — or even admirable and superior — by plausible means.[2] It is also an informal fallacy of reasoning.[3]

And another related and suitable defintion from the sociolgy field:

Rationalization (sociology) … In sociology, rationalization or rationalisation refers to the replacement of traditions, values, and emotions as motivators for behavior in society with concepts based on rationality and reason.

I think that all of these tend to fit and that where they intersect would suggest a specific period in time which marks a period of a great change. An era of an actual globally accepted money standard.

“In Transition to Optimal Standards”

Our view is that if it is viewed scientifically and rationally (which is psychologically difficult!) that money should have the function of a standard of measurement and thus that it should become comparable to the watt or the hour or a degree of temperature. And money, as an efficient practical means of transferring utility, naturally links directly with the game theoretic idea of “TU games” (games with transferable utility).~Ideal Money

Governments and banks are institutions that evolved out of the compounding insights of mankind throughout the ages. They are expressions of our extrapolations of our natural freedoms in relation to our observations on history and nature. They are held up by propriety-the will of the populations to which they serve.

To declare that technology and social advance would bring great value to the population but to suggest that the institutions that such a population upholds could act against its own mandate I think is to not understand the nature of such institutions.

We seem to somewhat collectively hold the belief that our governments are out to get us but I think this orientation can be seen to be simply a “religious fervor” probably most explainable by the realization that we don’t really understand what is “optimal” in regard to our global economy and respective local currencies.

Isn’t it quite “marxist” (in regard to the disastrous type of communism etc) and absurd to blame the institutions we created as if they are entities that function separately than the people that uphold their relevance?

Rather I think the problem of our global economy and the true cause of our traumatic stress syndrome is that historically we had no proper “sun” to orientate to and although gold is an example of the type of orientation we should want it did not provide a strong enough basis.

It is therefore why I think that the introduction of Bitcoin will make the problem of currency orientation quite “solvable” such that each nation and the constituents within it will put an unstoppable pressure on our evolution towards a single monetary standard.