# Bitcoin manifest in John F Nash Jr.’s two player games

To take things *“in your stride”* is to remain composed while dealing with irregularity, and has relevance to how committed a strategy becomes when faced with unexpected outcomes — there is a saying among market traders on solvency and rationality, where the latter outpaces the former, so that game theory assumes utility in understanding equilibrium or vantage points to a situation, where one feels they’re unable to play to any greater unilateral gain, benefit, or welfare, as defined by the payment episode in doing so.

Retrospection and hindsight are readily available in such plays, but in real time, the principle move is to look ahead and reason back. In bitcoin for example, the cryptographic nonce is used as singular communication so that old (communications) cannot be used in replay attacks.

# Two player games

The characteristic functions in von Neumann’s and Morgenstern’s *Theory of Games and Economic Behavior* (1944) were to take measurable utility and rational probabilities in games of strategy, which moved economics away from a predominate belief of a matter for human psychology of self interest, so quantities could be used to determine a strategic approach.

John F Nash Jr., then added four additional axioms (in The Bargaining Problem, 1950) comparable to von Neumann’s and Morgenstern’s work, which accounted for 1) invariance to scale; 2) Pareto optimality; 3) independence of irrelevant alternatives; and 4) symmetry.

In later game theory (*The Ideal Money* and *Agencies Method*) Nash is still considering an axiomatic approach. In Hierarchical Introspective Logics (1998), Nash is once again looking to answer unanswerable mathematical questions by finding a standing proof of a conjecture.

One might speculate at this time (the turn of the twenty first century), where the internet was beginning to become widely adopted, Nash realised there was an additional axiom to be added in such a proof *— inter-connectedness*, where computer networks make world wide communications and translatability an everyday occurrence, so that Nash’s work in non-cooperative games meant his equilibrium idea could now apply in pro-cooperative scenarios.

The idea therefore is that in two-player games, there is Player A (the rules, customs, culture and laws) and Player B (the subjects to Player A) where human interaction becomes a sub-set of Player B, and where all other axioms in The Bargaining Problem (1950) still hold, but with *inter-connectedness* now added.

# Irreversibility and bitcoin

It has been remarked how the opening passages of bitcoin address quasi-legal issues of mediation, fraud and reversibility, and how financial intermediaries can’t avoid becoming embroiled in dispute resolution, so that merchants become overly suspicious of their customers and clients in farming for more information about them than is necessary.

The systemic adoption of a characteristic function probability distribution — Satoshi took the time to explain how bitcoin satisfies the requirements of Pareto optimality — means bitcoin becomes representative to the agency of the type found in Player A games, so that majority decision making within Player B games becomes characterised as cooperative.

Further to this is the bitcoin representation of a steady and constant inflation schedule, such of the character which can be accounted for in contract indexation, so that if everyone is on the same page, the money unit at the heart of the contract can be standardised in the *n-person* (two player named persons with finite definition in probability) scenario, as to stride out irregularity reflected in the payment of contractual rewards von Neumann and Morgenstern envisaged residual in coalition formation.