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

“There have often been attempts by various students of history or writers on Economics to link times and places of good economic progress to cultural circumstances that might be imagined to favor, somehow, the good fortune.” John F Nash Jr., Ideal Money and Motivations of Savings and Thrift, 2012

John F Nash Jr. writes an afterword in *The Essential John Nash *(Kuhn and Nassar, 2002, *page 241*) where Nash acknowledges his sudden prominence (in 1994) to what is called “game theory”, upon which Nash starts attending meetings and becomes involved in a research project which Nash simply describes as “concerned with the realisation of the *Nash program*.”

Nash expands on this work as a project that by 2002, consisted of a considerable quantity of calculations, the value of which developed software such as Mathematica, used to study techniques of modelling contexts of bargaining and negotiation in terms of processes which can be investigated in terms of non-cooperative equilibria.

By 2003, Nash had spoken on how he had been using *Mathematica* in his “work on the game models of the type in agencies”, where the Agency Method was an experimental study in coalition formation which could be made possible through *contracts*, where verbal complications are eliminated from the various stages of coalescence in such agencies, and where the agency begins to assume something akin to a “power of attorney”.

The comparison has been made between the voluntary participation but irrevocability of such an election procedure outlined in the Agencies Method, with the bitcoin network, where nodes are free to join and leave the blockchain voluntarily, but can trust the globally shared view in their absence.

# Randomisation in Game Theory

John Nash’s Ideal Money — a theory on a money which is “intrinsically free of inflation” — was also being developed, simultaneously to Mathematica and The Agencies Method, with concern to the *“realisation of the Nash program”*.

For Nash, money assumed transferable utility in trading, and thus Nash’s Ideal Money can be seen as a logical and obvious extension to (Nash’s) earlier instigations in bargaining, cooperative, and non-cooperative games:

“Here we can return to the understanding that money has the practical value of creating games for traders that are games with transferable utility when without the money being available the game of the traders would be a game without transferable utility and thus naturally a game with less efficiency in relation to the possibilities for the participants of maximizing their combined situation of gains.” John Nash, Ideal Money, 2002

The ideal money was believed by Nash to assume a purpose in the performance and completion of contractual obligations, where for without such a reliable medium of exchange, the value of contracts would lose meaning, becoming comparable to a climate of lawlessness as a result.

Acquaintance with the mathematical technicalities of Nash’s work is not necessarily required to understand the formal representations being made: for example, in Two Person Cooperative Games (1953), Nash extended his previous treatment of “The Bargaining Problem” (1950) to a wider class of situations where threats can play a role and therefore introduced the elaboration of the threat approach.

In this work (Two Person Cooperative Games), Nash speaks of mixed strategies representing courses of action a player can take independently of other players, which may involve a deliberate decision to randomise and decide between alternative possibilities by using a (randomising) process involving specified probabilities.

Interestingly, in the Two Person Cooperative Games, Nash then makes this observation:

Some twelve months later, Nash then writes Parallel Control, constituting a futuristic insight into the electronic brains of the future, where trial, error, abstraction, and conditioning processes could lead to a *“genuine thinking machine”* and one which would decentralise control.

# The Lottery of Bitcoin Mining

Bitcoin is sometimes referred to a mathematical puzzle, because of the chance involved in being rewarded for mining bitcoin, even if the outcome to the puzzle is deterministic: we can predict with some certainty — a certainty which is influential in forming rational expectations and anticipation as to the bitcoin supply inflation mechanism, and therefore a reasonably grounded speculation as to how bitcoin might be priced — that by circa the year 2140, all bitcoin has been mined.

There seems therefore an obvious parallel between the ideas of randomness and probability between bitcoin and Nash’s work in *Two Person Cooperative Games* and *Parallel Control*: that the effect of what can be expected as probabilistic appears to derive from the cause of randomisation:

Satoshi Nakamoto described his bitcoin script as a predicate — or as an equation which evaluates to true or false, to support a tremendous variety of transaction types, from the basis of a lottery type reward process.

# Parameters of Negotiation and Software

Nash’s suggestion in Ideal Money that an appropriately honest-like government agency could come to issue the actual (ideal) currency, is not only redolent of Nash’s earlier comment on the need for an umpire to enforce contracts in Two Person Cooperative Games (1953), but also Satoshi Nakamoto’s observation on the inevitability of dispute resolution:

“Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes.” Satoshi Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System, 2008

With *Mathematica*, Nash was interested in finding equilibrium points for parties with deterministic opportunities for bargaining and negotiative actions (where an agreement or contract can be made), and for where each of the parties were not capable of making refinement to their strategic behaviour.

Nash found that the majority of this work was done with twenty one variables.

In respect of the microeconomic implications, this is interesting: contracts or agreements make use of inflation in respect of indexing an observable level of prices — contracts or agreements being the cornerstone and distinguishing property for cooperative games — so that if an ideal money (money with a steady and constant inflation), became considered accepted as the basis for contractual indexation, for which Satoshi intimates it was — then a conservative form of investing becomes possible:

In respect of the opening remarks regarding times and places of favourable economic fortune being linked to cultural circumstances, Nash may have been implying that such luck might apply to the two-person zero sum scenario, but need not occur in general.