Law and Justice in John F Nash Jr.’s Ideal Money and Bitcoin

Jon Gulson
3 min readDec 20, 2020

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The opening passages of the bitcoin white paper address problems of fraud and dispute mediation which are regarded as inevitable where commerce on the internet has come to rely exclusively on financial institutions serving as trusted third parties to process electronic payments:

“A certain percentage of fraud is accepted as unavoidable.” Bitcoin: A Peer-to-Peer Electronic Cash System, 2008

Indeed, it becomes a small psychological jump from thinking a certain percentage of fraud is accepted as unavoidable TO a certain percentage of fraud is acceptable, in forming anticipations and expectations of the law, justice, and regulatory environments by which money assumes utility and value.

Law and Justice in John Nash’s Game Theory

After a three decade absence due to mental illness, John F Nash Jr. resumed his earlier work in game theory, with the Ideal Money and Agencies Method.

Game theory distinguishes a cooperative game and non-cooperative game as one where binding agreements or deals can be made, thus inducing cooperation, and before Nash’s work in the 1950’s, economists assumed two-way bargaining was determined by psychology.

In the anticipation of no co-operation, Nash went on to formally define an equilibrium where “a configuration of strategies, such that no player acting on his own can change his strategy to achieve a better outcome for himself”.

When building on his earlier contributions, Nash developed a system where the anticipations and expectations of players in co-operative or non co-operative games became a demand, and one where Nash started to consider pro-cooperative games:

“…players of a REPEATED game of “prisoners’ dilemma” can have a good cooperative equilibrium (in an infinitely repeated game context) where each player has, strategically, a DEMAND that the other player should play in an approved cooperative fashion (thus a fashion not betraying either prisoner to the adverse judgment of the police and magistrates).” John Nash, Agencies Method, 2010

In the Ideal Money, Nash describes the application of such a money (with a stability of value) to be “particularly of benefit in connection with contracts or exchanges involving long time periods for the complete performance of the contract or exchange”:

“To have the better sort of a money in use (combined also, perhaps, with a good culture of procedures of law and justice, and with public transport vehicles running on schedule, and electricity supplies of ample quantity and good reliability) will naturally tend to favor economic progress and, in the long run, higher living standards for the human population”. John Nash, Ideal Money and Asymptotically Ideal Money, 2010

Why Proof of Work Matters

The bitcoin forking wars are based around propositions of decentralisation, trust models, and transactional efficiencies, removed from Satoshi Nakamoto’s original view on which chain is the most valid:

“Proof-of-work has the nice property that it can be relayed through untrusted middlemen. We don’t have to worry about a chain of custody of communication. It doesn’t matter who tells you a longest chain, the proof-of-work speaks for itself.” Satoshi Nakamoto, 2010

In the second problem bitcoin says it solves — that of determining representation in majority decision making — it becomes clear, bitcoin is cash in a legally defined sense it can’t be litigated on — reversed — because of its time-stamping, and such time-stamping represented in the bitcoin inflation proposition, as steady and constant.

Bitcoin describes how to take the profit out of cheating by using escrow or using bitcoin as the basis for bonded contracts, so in respect of law and justice and bitcoin there is no reliance on recourse, it’s all prevention.

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