# Bitcoin As An Implementation of John Nash’s Asymptotically Ideal Money

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.~Nash Ideal Money

Peter Todd explains a concept that is cited to first have been explained on a reddit post 6 or so years ago:

This article will show that a fixed block reward does not lead to an abundant supply. In fact, due to the inevitability of lost coins, a fixed reward converges to a stable monetary supply that is neither inflationary nor deflationary, with the total supply proportional to rate of tail emission and probability of coin loss~https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary

Simply put if we assume that coins are lost at a % based rate the actual coins lost over time will converge with any chosen monetary inflation rate.

It’s hard to put it in an easy to read way-here Ruben Somsen tries:

Tail emission is defined as a fixed block subsidy, meaning that it does fluctuate as a percentage of total circulating supply, and does not fluctuate in absolute terms.

Coins lost per year is assumed to be a proportion of circulating coins, meaning that it does fluctuate in absolute terms, and does not fluctuate as a percentage of total circulating supply.

A similar and more basic observation can be made I think. If newly added units are supplied at a constant rate the corresponding % they increase the total supply by decreases accordingly.

This % limits to zero. But it doesn’t get to zero.

Todd is just adding the fact that coins get lost on top of this convergence-to-zero.

There is a problem for the issuer of a currency, whether in coinage, paper, or electronic form, that if this currency (or money) is too good, then it could be exploited by all sorts of parties and interests…

There is the observation that, in regard to the effects on an economy, a limitless rate of newly supplied units can be absorbed in contract formations:

….simply to improve the conditions under which agreements regarding long-term lending and borrowing would be made, a money would be more or less equivalently good if it had a completely steady and constant rate of inflation. Then this inflation rate could be added to all lending an borrowing contracts. Hence, the problem of a money that would be too good is avoidable.

That is to say if a money is known to be expected to lose 2% of its value throughout the length of a contract, then the lender might add 2% interest to the (re-)payment of the loan in order to perfectly counter balance the loss.

Here it’s interesting to think about the emissions observation and Satoshi’s decision to introduce a finitely supplied bitcoin.

What Todd has really pointed out is that in either scenario of a tail emission or a rate that has an issuance deadline the total supply of coins trends towards an asymptote.

Look at the precise words Mario Gibney uses:

Peter Todd recently published a mathematical demonstration for tail emission in bitcoin-like coins resulting in an effectively capped circulating supply

He uses the word effectively because technically its an asymptotic/limit based observation.

Philosophically viewed, bitcoin does have an infinite supply as we could continue to divide the supply rate by 2 every four years theoretically (and never actually reach zero but always closer to it).

For all this we have shown that the question of finiteness of the supply, in regard to the choice of the supply rate, is essentially arbitrary, based on the asymptotic nature of the issuance.

Of course there is also the “psychological” aspect to think about:

..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?

What is interesting here then is if we define Ideal Money as:

…money intrinsically not subject to inflation…

and that:

It is only really respectable that there should not be an arbitrary or capricious pattern of inflation,

Then this all gives a different perspective from which to understand the concept Nash presents as ‘asymptotically Ideal Money’:

To me it seems a striking paradox that central bankers and their economist advisers can think in terms of having a “targeted” rate for inflation without realizing that that rate should be zero!

This paradox, or my perception of it, was what led me to the concept of “Asymptotically Ideal Money”. Suppose that there were, formerly, “free Keynesians” and then, later, there came to be “restrained Keynesians” whose freedom to freely issue additional money and credits however they might please to do so would have become a bit restrained by the need to support a doctrine of targeted inflation.

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