# Pareto in John F Nash Jr.’s Ideal Money and Bitcoin

Inchoate in probability is the idea for the determination of the bargaining situation or game by evolving an intuition as to what constitutes value for money in the outcome.

The intuition is influenced by the variant and invariant, and over time iterative and recursive, so that the game or situation can appear indeterminate.

Theorising such games moved toward anticipation of strategic propositions, rather than two person scenarios summing to zero. In their book Theory of Games and Economic Behavior (1944), John von Neumann and Oskar Morgenstern invited a breaking of the mould.

# Made in Austria

John von Neumann contributed most of the mathematical insights in the book, while it was Oskar Morgenstern who provided the economic theory for the structure of the problems — Morgenstern had been a student of Ludwig von Mises while in Austria, and succeeded Friedrich Hayek in 1931 as the director of the Institute for Business Cycle Research in Vienna — before emigrating to the United States and taking an economic position at Princeton University.

Bert F. Hoselitz was also a student of von Mises in Vienna, before himself emigrating and teaching a course in International Economics (1947–48) at the Carnegie Institute of Technology, where incidentally John F Nash Jr. was a student (and the only economics course Nash took before achieving his pathbreaking work in game theory and bargaining at Princeton University in the early 1950's).

# Sold in Princeton

There exists a belief therefore the underpinnings of game theory derive from Austrian economic thought, in finding a determinative strategy between economic players rendered agents in a mathematical game.

The departure in John Nash’s The Bargaining Problem (1950) from von Neumann and Morgenstern lays in Nash’s adoption of an axiomatic method, and that the reason for indeterminacy in such a bargaining game is the bargaining players wouldn’t have enough information on their preferences, so Nash realized he had to make additional assumptions.

Nash asked the question of the reasonable conditions any solution or split would have to satisfy? He then used four conditions, which if held, showed a unique solution existed, the second of these conditions being Pareto optimality.

# Pareto

“Pareto efficiency or Pareto optimality is a situation where no individual or preference criterion can be better off without making at least one individual or preference criterion worse off or without any loss thereof. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution.” Pareto efficiency (Wikipedia)

Pareto is sometimes known as a principle of the 80:20 rule, whereby 80% of consequences derive from 20% of causes (or the law of the “vital few”).

This has broad and general applications, and has even become memetic in social media:

John F Nash Jr., some half century after his work in The Bargaining Problem, again uses Pareto in The Ideal Money and also in his Agencies Method, as a way of reaching an equitable solution to money used in optimising consensus in transferable utility.

# The Power Law in Bitcoin

The Power Law is understood as a functional relationship between two properties — and according to Wikipedia — where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.

The power law can be shown graphically in relation to bitcoin inflation over time:

In relation to the long tail of the Power Law, the relationship between bitcoin and the sovereign issued monies is clear:

# Probability in determination

There is an exchange involving Satoshi Nakamoto on the mailing list in July 2010 about payment processing, where Satoshi explains how bitcoin positions itself in network propagation, and where the network is working with the 80:20 rule:

There is a further posting from Satoshi, in response to a criticism that bitcoin isn’t impermeable, where Satoshi’s response is to agree, with the implication that bitcoin network propagation is based more on probability than perfection:

“I didn’t say impermeable, I said good-enough. The loss in practice would be far lower than with credit cards.” Satoshi Nakamoto, 18 July, 2010.

This is significant for no reason other than showing the probability for the 21 million coin issuance limit in bitcoin, is it satisfies the axiom of Pareto efficiency.

It is also relevant to John F Nash Jr.’s work in Ideal Money, where Nash expresses a distrust in central banks because of his belief they work with an insufficient axiom set in relation to an expectation of the users of sovereign issuance: a problem he showed solvable in The Bargaining Problem (1950), by introducing Pareto efficiency (as an axiom).

This relationship and commonality between Nash and bitcoin is also strengthened by the citation of William Feller — who Nash would have known from his Princeton days in the 1950’s — in the bitcoin paper and Feller’s work in probability theory.

We have too, in summation in the mathematics of bitcoin in the paper before its conversion to code (page 7), Satoshi’s intention to avoid summing the infinite tail of the distribution: an acknowledgement, it seems, to the second problem bitcoin states it solves — being deterministic in representation of majority decision making — as to form a realistic expectation as to where bitcoin has come from and why.

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## Jon Gulson

Ideas in games, language, and trust.