Cooperative Propagation in John F Nash Jr.’s Ideal Money and Bitcoin
In a mailing list post of November 2008, Satoshi Nakamoto — the pseudonymous creator of bitcoin — agrees cryptography can’t solve political problems, but points to the possibility of it “winning a major battle in the arms race”, gaining “a new territory of freedom for several years”:
“Governments are good at cutting off the heads of centrally controlled networks like Napster, but pure P2P networks like Gnutella and Tor seem to be holding their own.” Satoshi Nakamoto, 6 November, 2008
In a later post, Satoshi Nakamoto repeats the “race” analogy, in respect of how his system design works:
“When you broadcast a transaction, if someone else broadcasts a double-spend at the same time, it’s a race to propagate to the most nodes first. If one has a slight head start, it’ll geometrically spread through the network faster and get most of the nodes.” Satoshi Nakamoto, 17 July, 2010
Around the same time, Satoshi Nakamoto posts on the generality of his original design, to avoid the problem of having an explosion of specialised use-cases (but which could be supported later on):
“…I wanted to design it to support every possible transaction type I could think of. The problem was, each thing required special support code and data fields whether it was used or not, and only covered one special case at a time. It would have been an explosion of special cases. The solution was script, which generalizes the problem so transacting parties can describe their transaction as a predicate that the node network evaluates.” Satoshi Nakamoto, 17 June, 2010
Satoshi Nakamoto then refers to his design as not being new to him:
“The design supports a tremendous variety of possible transaction types that I designed years ago.” Satoshi Nakamoto, 17 June, 2010
Suggesting he was an older gentleman experienced in the field of decentralised cryptographic system design.
The RAND Corporation
The Second World War (1939–1945) has sometimes been described as the mathematicians war because as Germany rearmed, it also made sure it built secure communications, knowing one of the reasons it suffered significant losses among its submarine fleet in World War 1 (1914–1918), was due to the Allied forces breaking German ciphers and codes.
The story of how Germany then built an Enigma machine, subsequently cracked by Alan Turing, has been told in the film The Imitation Game, and after the end of the war, there was an interest in using game theory applications to solve problems of military strategy, where the RAND Corporation think tank is probably best known.
Game theory was also being used at this time to understand bargaining problems and games of an economic character, which came to be associated with mathematicians at Princeton University, including Lloyd Shapley, John Von Neumann, Harold Kuhn and John Nash — where some also worked at RAND, whose scientists were thought the alleged models for Stanley Kubrick’s film Dr Strangelove, along with its references to Operation Paperclip and the recruitment of former Nazi scientists, engineers, and technicians by the Americans to help them win the post second world war arms race.
The Bargaining Problem
The problem of bargaining in economics and using mathematics to solve it, revolves around the idea that both (economics and mathematics) deal in quantities, and up until this time (1944–1950), had previously been thought indeterminate, in that knowing the bargainers preferences doesn’t necessarily predict how they will interact or arrive at a pay-out.
John Von Neumann and Oskar Morgenstern became known as the founders of game theory, with their work in Theory of Games and Economic Behavior (1944) regarded ground breaking text in suggesting the answer lay in reformulating the problem as a game of strategy, while not succeeding themselves in solving it.
John F Nash Jr. then took up this problem, not by defining a solution directly, but by adopting an axiomatic approach, and his paper The Bargaining Problem (1950) is thought to be one of the first to apply the axiomatic method to a problem in the social sciences.
Nash’s theory assumes both sides expectations about each others behaviour are based on the intrinsic features of the bargaining situation itself. He started by asking what reasonable conditions would any solution or split have to satisfy?
He then showed if the axiomatic conditions held, a unique solution were possible.
Generality in John Nash’s Ideal Money and Bitcoin
The generality of Nash’s method in the Bargaining Problem became repeated in his later works, including Non-Cooperative Games (1951), which is a generalisation of the concept of the solution of a two-person zero-sum game, based on the absence of coalitions, as it is assumed participants act independently of each other and without communicating.
Nash was persuaded to include a specialised example in Non-Cooperative Games of a three man poker game, despite his initial resistance. A parallel can be drawn with Satoshi’s comments on the generalised nature of the bitcoin core design, which was believed to contain a poker client in its pre-release code, but then dropped.
Also in Ideal Money, which is an extension of Nash’s earlier game theory in bargaining, there is reference to money only existing because of the specialisations of divided labour:
“And philosophically viewed, money exists only because humanity does not live under “Garden of Eden” conditions and there are specializations of labor functions.” John F Nash Jr., Ideal Money and Asymptotically Ideal Money, 2003
Nash notes in his Ideal Money — in the manner of his approach in The Bargaining Problem — to a distrust of central banks, because of their approach to inflation containing an insufficient set of axioms i.e. the expectancy the money users have in relation to future stability of value.
John Nash’s Note to RAND
Generality is also referenced in a proposal Nash sent to RAND in August 1954 for the architecture of a parallel computer, which had the simple aim of decentralising control in a computer system, (drawing obvious comparisons to Satoshi’s remarks on the limitations of centrally controlled networks and to what he designed “years ago”):
The utility of such a decentralised network in communication in both military strategic and bargaining settings, in cooperative propagation in decision making, is implied by Nash in Parallel Control:
Representation
By 1951, Nash had introduced the distinction between cooperative and non-cooperative games: cooperative games being those in which players can make enforceable agreements with each other (such as contracts) and fully commit themselves to specific strategies.
In contrast, non-cooperative (or competitive) games are absent of enforceable agreements as it is difficult for players to communicate with, and trust, each other.
In later works (circa 2003 onwards) in Agencies and Cooperative Games, Nash works on an idea of contractual coalescence which is based on the representation of attorney agents through a computational method, which intends to remove verbal complications in the representation of the bargainers.
Theoretically at least, and in relation to the bitcoin blockchain, there is the possibility this representation can conflate the two different game forms (cooperative and non-cooperative) due to its openly observable nature, and by inducing players onto the same standard, becoming useful as both an indices or medium in contracts — and to which Satoshi was specific on such utility — where other inflationary measures such as Consumer Price Indexes are adopted, and also as an inflation hedge or savings media.
If true, the idea of “scaling” in bitcoin becomes a reference to cooperative propagation, and to where, in Satoshi’s words, a new territory of freedom can be gained for several years.
