Nash (far left), Shapley (centre right).

How the Shapley value makes bitcoin “intrinsic”.

Jon Gulson
Rustbelt Innovators
3 min readJul 13, 2022


A recent twitter direct message exchange veered into the possible relationship between geopolitics and thermodynamics.

This provoked a few thoughts on the nature of bitcoin and how it might take “physical” form, which seems like “hot air” in the humorous sense of what’s common to both geopolitics and thermodynamics!

All this might read nonsensically, since bitcoin doesn’t assume physical form in the usual monetary representation of coins or notes. There is an observation to be made regarding criticisms of bitcoin in that a) bitcoin isn’t considered to hold any intrinsic value at all; and b) bitcoin energy consumption is believed “wasteful” in that it’s creating an externality serving no obvious purpose or benefit beyond private speculation.

Satoshi himself admitted bitcoin mining was “wasteful” in a thread on the thermodynamic perversity of its minting, but that the utility of exchanges bitcoin makes possible exceeds the cost of electricity used — in other words, the externality is positive rather than negative.

It might be concluded from this, that this externality is in fact the intrinsic value to bitcoin — money ideally shouldn’t hold any other value or agency than to serve as media between bargaining agents, and if we push this further, we can exam what appear to be game theoretical principles behind the bitcoin design.

Is bitcoin hashing the Nash program and Shapley value?

It has previously been written how bitcoin can be understood as an extension and implementation of John F Nash Jr.’s game theory and bargaining idealizations:

Bitcoin as an Implementation of John Forbes Nash Jr.’s Axiomatic Bargaining “Idealizations”. | by Jon Gulson | Rustbelt Innovators | Medium

Like Nash, Lloyd Shapley was a Princeton University game theorist whose work in the 1950’s later won him a Nobel prize in economic sciences, and the Shapley value which he introduced, like Nash’s work, is characterized by a collection of desirable properties as a solution concept.

These characteristics or conditions are:

  1. All the gains from cooperation are distributed among the players — none is wasted.
  2. Players that make equal contributions receive equal payoffs.
  3. The game cannot be divided into a set of smaller games that together achieve greater total gains.
  4. A player that makes zero marginal contribution to the gains from cooperation receives zero payoff.

Intrinsic by design

Returning to the question of what’s intrinsic about bitcoin, we can consider the axioms required in the Shapley value as present in the bitcoin hashing protocol and unspoken rules which govern bitcoin mining, and where the Shapley value’s computational complexity is exponential in the number of players thanks to the intrinsic difficulty mechanism contained within bitcoin.

For example, Satoshi assumes with time more people add computation power to the bitcoin network and bitcoin is therefore distributed to them as reward:

“Coins have to get initially distributed somehow, and a constant rate seems like the best formula.” Satoshi Nakamoto, 2008

If too, bitcoin is considered as game theory writ large, it presents possibilities and potential for these design features to become “intrinsic” (or axiomatic) to future evolutions of cryptographically orientated money, which over time could induce cooperation across an optimal geographical basis (a one world coalition) by being used as indexation or adjustments in contracts, which of course are a cornerstone of cooperative game theory and how parties to the bargain can experience welfare from a commonly agreed plan of action or campaign.