A Response to Goodwin and Webb
Identity in blockchain technology is a question which can go in different directions. This article is written in response to Mark Goodwin’s and Whitney Webb’s co-authored blog post The Chain of Issuance (August, 2024) which raises concerns around surveillance in patented and privatised blockchains threatening user privacy through centralised control. Specifically this article is concerned with game theory and the symmetry required for cooperation in networks and how this might assuage the fears Mark and Whitney express.
The intention here is to show how the original blockchain of Bitcoin contains a priori properties (axioms) which render other blockchains meaningless unless satisfying these conditions. Firstly however, let’s begin by summarising The Chain of Issuance.
The Chain of Issuance
Goodwin’s and Webb’s blog opens with a description of quantitative data becoming the most liquid market on the planet and how it’s used to predict consumer spending and other behaviours so that infrastructure providers like technology companies assume over-importance and too much influence. In regards to finance, Goodwin and Webb are concerned a cabal of incestuous conspirators co-opt blockchain technology for their own selfish ends and circumnavigate even the government in this.
The Chain of Issuance is a lengthy and exhaustively researched article. If one were to condense the article to a game theoretic conclusion, it’s essentially saying the oligarchs of technology and big finance hold a distorted and unnatural bargaining position.
It is here we introduce the dichotomy between non-cooperative (zero sum) and cooperative (non zero-sum) games and how they apply to the identity and privacy issues.
Randomisation
Before Oskar Morgenstern partnered with John von Neumann on their famous book Theory of Games and Economic Behavior (1944), Morgenstern reflected on a puzzle presented in Conan Doyle’s short story The Final Problem where Sherlock Holmes tries to outsmart his criminal arch-rival Moriarty, but has difficulty in this because both Holmes and Moriarty are rational twins where complexity arises from their symmetry. The only solution to break this symmetry is to introduce randomness, making it difficult for either Holmes or Moriarty to predict the next move of each other. Morgenstern and von Neumann took this up as a game of strategy and modelled it as a zero-sum game (adversarial) in the form of matching pennies.
This randomness was thought to be “arbitrary” and troubled the early bargaining theory pioneers like John Nash where the goal was to reach a nonzero-sum outcome (cooperative) of how to divide a set of goods where no party has any antecedent claim and where any mutually agreed upon decision will be binding.
John Nash articulated a solution to this in his first game theory paper The Bargaining Problem (1950) which determined the amount of satisfaction each individual should expect to receive from the situation, or a determination of the worth to each individual(s) having the opportunity to bargain.
Nash’s bargaining solution uniquely satisfies four simple axioms, one of which is symmetry. And one where the problem can take on especially simple form when represented by small amounts of money and is a symmetric solution because it does not vary on the names or the labels of the bargainers involved.
Symmetry and Blockchain
Symmetry is similar to the Holmes-Moriarty problem in that both parties are equally rational and well-informed. Symmetry also rules out any asymmetrical solutions.
Nash initially defines symmetry as equality of bargaining skill, but later (in Two Person Cooperative Games, 1953) acknowledges this term “suggests skill in duping the other fellow” and that haggling is usually based on imperfect information. Nash therefore makes an assumption in Two Person Cooperative Games of complete information:
“Each player is assumed fully informed on the structure of the game and on the utility function of his co-player (of course he also knows his own utility function).” John F Nash Jr., Two Person Cooperative Games, 1953.
In one of Nash’s later works The Agencies Method for Modeling Coalitions and Cooperation in Games (2008), he says the “agency” of each player can just be accepted — i.e. we do not need to farm for information or personal data to reach agreement or the opportunity to transact. This chimes with Satoshi Nakamoto’s reductive observation of the problematic need for trust:
“Merchants must be wary of their customers, hassling them for more information than they would otherwise need.” Satoshi Nakamoto, Bitcoin Whitepaper, 2008
The simple conclusion reached here is that private, patented, or permissioned blockchains can’t work because they are asymmetrical to the idea of distributive justice in a bargain or contract. They tend to be non-cooperative by nature because they don’t work to a sufficient set of assumptions, whereas Bitcoin tends to incentivise cooperation because the rules and structure of the “Bitcoin game” are clearly laid out and transparent and where the pseudonymity involved doesn’t require first person identity. It’s for this reason the chains of custody Goodwin and Webb write about, are not built from solid foundations. Moreover, it suggests the architect of Bitcoin was unusually familiar with established game theory.
