John F Nash Jr.

The Game Theory Behind the Bitcoin Genesis Block

Recent writings have surmised on the proposition bitcoin is a logical extension and implementation of John F Nash Jr.’s game theory and his “Ideal Money” and Agencies method for modeling cooperative games through coalition formation.

Nash’s early work in game theory resolved the problem of determination in economic interaction. Prior to this, economists and mathematicians recognized their respective subject matters holding the shared characteristic of quantities, and realized this characteristic could be rendered strategic, but until Nash’s mathematical proof in game theory, struggled to express such strategy as deterministic for n-player games (games with an arbitrary quantity of numbered or named players).

Four axioms were introduced in solving the bargaining problem:

  1. Pareto efficiency
  2. Symmetry
  3. Scale Invariance
  4. Independence of irrelevant alternatives

The Pareto Paradox in Bitcoin

While symmetry (the blockchain), scale invariance (difficulty adjustment), and independence of irrelevant alternatives (central banks), are all apparent in bitcoin, it is perhaps the presence of Pareto efficiency which is the most obvious parallel to draw between Nash’s game theory and the bitcoin network: bitcoin inflation density adheres to the 80:20 Pareto power law, which presents a paradox in that the further bitcoin “long tails” (through price increases) against the sovereign money issuances, the more bitcoin becomes “trivial” as defined by the Pareto rule (bitcoin) appears to contain as a design axiom in emphasizing supply side economics.

This is interesting in understanding the bitcoin value proposition, because the decentralization behind bitcoin presents problems to sovereign states in regulating, or banning, bitcoin. Such action — to be effective — would require enforceable multilateral coordination.

If this kind of coordination were possible, other problems requiring enforceable multilateral coordination i.e. climate change, international trade, and international dispute resolution, would also presumably become “trivial” by the Pareto definition.

It doesn’t seem probable a coalition (in the game theoretic sense) would form on this basis, but it seems possible a sovereign agency or agencies might experiment in subjecting bitcoin to the “Pareto” rule, such that a game of hashing signatures is created to be useful in indexation as coinage or a money unit in contracts, so that coalitions become enforceable through the terms of those contracts.

This contextualizes the bitcoin Genesis Block, also known as Block 0 — the ancestor that every other bitcoin block can trace its lineage back to, since every bitcoin traces back to a past one — as something of a mystery since the coins in the block remain un-spendable — suggesting bitcoin was the work of a benevolent actor who was making a move by nature, i.e. a decision or move in an extensive form game made by a player who has no strategic interests in the outcome.

The effect is to add a player, (‘Nature’), whose practical role is to act as a random number generator. The other paradox being bitcoin then simultaneously becomes random and deterministic and analogous to the first nature of a genesis, while using arithmetic as a function in a world where human beings mostly exercise verbal communication.

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Jon Gulson

Jon Gulson

Ideas in games, language, and trust.