Why Side-Payments need not be a “Special Consideration” in a Peer-to-Peer Cash System.

John von Neumann and an early computer, Princeton, 1945.

In its introductory paper, bitcoin subtitles itself an electronic peer-to-peer cash system, which is not a conventional representation of cash in traditional or physical form, and so causes much discussion and debate around the transactional properties of bitcoin as measured by factors such as settlement time, fee efficiency, security, energy consumption, and privacy — all synonymous with bitcoin “scaling” in context to payments and to the nature of money as media.

Beyond this however, lays a different understanding or consideration which might permit insight into the origins of bitcoin: that the bitcoin design is axiomatically deterministic from four fundamental bargaining features.

Bitcoin as Atonement on the Origins of Game Theory

John F Nash Jr.’s biographer Sylvia Nasar, in her 1998 book A Beautiful Mind, lays out how Nash, at Princeton University in the late 1940’s, became aware of a new branch of mathematics called game theory, to construct a systematic theory of rational behaviour by focusing on games as settings for human rationality.

John von Neumann was the first to provide a complete mathematical description of a game and its relevance to economic welfare and to prove a fundamental result (the min-max theorem). Von Neumann’s work was still incomplete however, as it couldn’t prove a solution existed for all games.

The reason for the indeterminacy became obvious to Nash in that additional assumptions had to be made to show unique solutions were possible. It is interesting therefore that the axioms Nash introduced in The Bargaining Problem (1950) also appear present in bitcoin, along with a reference to another Princeton mathematician of that period (William Feller), in that bitcoin is a probability based system, and that through the evolution of computing technology, bitcoin might be atonement for Nash in reconciling his non-cooperative ideas with von Neumann’s belief in coalitions and the power of contracts.

Four More Reasons John F Nash Jr. was Satoshi Nakamoto

While speculation can be made on such suppositions, what can be observed are Nash’s bargaining axioms in bitcoin, together with the many shared characteristics of Nash’s later game theory (Ideal Money and Agencies) with bitcoin, incidentally all released around the same time:

  1. Pareto Efficiency: The culminative supply of bitcoin and its inflation density both demonstratively observe characteristic functions of Pareto efficiency, and it appears the long tail distribution in bitcoin was a conscious design decision, with Satoshi apparently familiar with the 80:20 Power Law associated with Pareto, that it’s understandable Satoshi would want to get the majority of coins into circulation as quickly as possible, without becoming concerned about inequity.
  2. Symmetry: The pseudonymity in bitcoin provides symmetry, in that there isn’t an emphasis on identity because of the open source nature of the system.
  3. Invariance to Scale: The difficulty adjustment mechanism in bitcoin means that supply is kept “steady and constant”, so that rational expectations can be made as to how bitcoin might perform over time, no matter how much energy is or isn’t consumed in the mining process or directed to the network.
  4. Independence of Irrelevant Alternatives: The invariance to scale also means the supply schedule isn’t influenced by central bank debasement or characterised by an “arbitrary” approach to inflation.

In Two-Person Cooperative Games (1950), Nash differentiates his approach to von Neumann through the idea of determination, in that it is determination (and not “side-payments” which require “special consideration”) to really matter in a game theoretically based solution:

John F Nash Jr.

Beyond the first problem bitcoin says it solves (the fraud of double spending electronic coins), is the second problem it says it solves of determination (in representation of majority decision making), so that if bitcoin is an implementation of Nash’s Ideal Money, then such a media might succeed as a bargaining solution to modelling coalitions through readily trustworthy contract indexation (“cash”), rather than primarily a mechanism for side-payments.




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Jon Gulson

Jon Gulson

Ideas in games, language, and trust.

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