Orange core.

Ranking Preference: Ideal Money and the Anti-Game-Theory of Bitcoin Forks.

Jon Gulson


“The nature of Bitcoin is such that once version 0.1 was released, the core design was set in stone for the rest of its lifetime.” Satoshi Nakamoto, June, 2010.

Why is Bitcoin Core, called Bitcoin Core? This seems a question worth asking since forks from the original chain (BTC) are common, each with a value proposition of their own. However, Satoshi explains the most “proofed chain” (BTC) will always be 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, August, 2010

In this writing, “untrusted middlemen” are considered a representation of “Independence of Irrelevant Alternatives” (where in a peer-to-peer or two-player system, third parties become irrelevant); and with “Core” representative of Core Game Theory, a cooperative idea where the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition (in our case here, the most proofed chain of Bitcoin).

“Irrelevant Commodities” in Relation to John Nash’s ICPI Proposal

John Nash’s The Bargaining Problem (1950) is a paper derived at from a set of axioms or idealisations which are used to generalise a solution in a two-player game so that each bargainer receives a determination of the amount of satisfaction or expectation from the situation, or, rather, a determination of how much it should be worth to each of these individuals to have this opportunity to bargain.

Further in his development of bargaining, Nash then devises an ICPI (International Commodity Price Index) but without formally defining which commodities or consumables should be included in his index. This is presumably because of Nash’s awareness that heterogeneity of commodities are the source of well-known problems in comparisons of living standards across space and time which would make certain commodities “irrelevant” in context to taste and preferences.

This means on an international scale, ranking the preferences of individual commodities becomes problematic. For example:

“Japanese preferences over the various kinds of sheep cheese from different valleys in the French Pyrenees are hardly known, and it is no wonder that reforms in Japan are not evaluated on the basis of the local population’s preferences over these varieties of cheese.” Do Irrelevant Commodities Matter? Fleurbaey and Tadenuma, Econometrica, 2007.

Satoshi’s Generalisation

Just as Nash introduced an axiomatic approach in The Bargaining Problem because he realised he doesn’t know enough about each player preference, Satoshi explains how he couldn’t satisfy each individual use in his Bitcoin design and so adopts a similar approach to Nash’s bargaining solution:

“The solution was script, which generalizes the problem so transacting parties can describe their transaction as a predicate that the node network evaluates. The nodes only need to understand the transaction to the extent of evaluating whether the sender’s conditions are met.” Satoshi Nakamoto, June, 2010

Satoshi, in the same post, then goes onto explain how this would be useful in supporting a wide variety of transactions, such as bonded contracts, third party arbitration, multi-party signature etc. He was also making the electrical consumption of BTC’s proof of work a characteristic function of the design in the extensive form Merkle Tree so that the grand coalition of the core is maintained, disregarding the need for a trusted middleman.

John Forbes Nash Jr.’s Ideal Money Proposal

John Nash’s Ideal Money is still a relatively little known area of work in context of his better known contributions to cooperative and non-cooperative game theory. It is notable that Nash himself admits to the wide topic of “money” being prone to psychological and subjective interpretation, making objective analysis — in the way we may reason about a technology — difficult.

Originally, Nash had the ICPI idea as the basis for his Ideal Money proposal, but later hints that it was only by indexing electric energy that the Ideal Money would have proper value:

“When I spoke at an economics meeting in Tampa, Florida, in 2001, on the topic of “Ideal Money”. I suggested the use of an “ICPI” index for the definition of the proper value for an “ideal” money. Here ICPI stood for “Industrial Consumption Price Index” (which would be a sort of index which could naturally be calculated from world market prices). But I did not have any specific proposals, like prices for copper, or platinum, or electric energy to suggest for the index.” John F Nash Jr., Ideal Money and the Motivations of Savings and Thrift, 2011.

Nash, in the same paper, concedes some discretion to a third-party like arbitrator (ironically violating Independence of Irrelevant Alternatives), but in the context that such a third-party has been laid open to greater transparency in respect of its representative privilege:

“Now, after some years of thought and observations, I feel that the sort of authority or agency that would be able to establish any version of ideal money (money intrinsically not subject to inflation) would be necessarily comparable to classical “Sovereigns” or “Seigneurs” who have provided practical media for use in traders’ exchanges. We can prepare to appropriately respect the functioning of such an agency (conceivably like the IMF or BIS or ECB) and concede to the effective agency some discretion about the specific form of a guiding index of prices. But here is where I see the importance of honesty, as if like the honesty of a well-regarded classical European monarch or emperor.” John F Nash Jr., Ideal Money and the Motivations of Savings and Thrift, 2011.

BTC: Born Immaculate?

The anonymity (or pseudonymity) in Bitcoin allows the exploration for the possibility of social ordering functions. For example, in a two-person game where the agents have the same preferences making the two peers indifferent to alternatives. Applying this to the case of macroeconomics, the central bank can become irrelevant:

“If it becomes a matter of strong and definite preferences that the money used should have definite characteristics of quality then, in principle, the people can demand that.” John F Nash Jr., Ideal Money and Asymptotically Ideal Money, 2008.

To overcome the limitation of commodities and their irrelevance in atomised locations of trade, there are the concepts of characteristics and functions which give a wider translation to the individual commodity through the idea of a composite or synthetic commodity. This means “core” dimensions can be estimated; if, for example, we take the example of French mountain cheeses and Japanese sake, we know the basics of functioning satisfying calorie demand, nutrient value, entertaining in social settings, etc; are the same whether in France or Japan.

Game theoretically, Nash expresses this in “characteristic function”:

“There has been a tendency…to describe a sample game simply by specifying its characteristic function. We wish to call such a game, for which an underlying “normal form game” or “extensive form game” has not been specified, a “CF game”. John F Nash Jr., First Report on a Project to Study Cooperation in Games by Means of Modeling in Terms of Formally Non-Cooperative Action in a Repeated Game Context, 2001

To generalise this, the space of characteristics or functioning might be as diverse as the space of commodities — but by focusing on the core characteristics — in the way Bitcoin proof of work prices the electric energy required for any kind of industrial consumption — a measurement can be made on the prospects for welfare independent of boundaries.

And interestingly, over time, Bitcoin forks lose their value against the majority chain. One may posit this is because BTC satisfies the majority preference as to how it is represented and which spans much further than traditional election, business, or contractual cycles. The Nash bargaining axiom of Independence of Irrelevant Alternatives is rich subject matter in relation to Bitcoin in this regard.