Did Bitcoin Arise from the “Nash Program”?
This article eventually answers its own rhetorical question in the positive, i.e., that Bitcoin indeed arose as a result of the Nash program. The justification for this is based on circumstantial reasoning around the Nash program and the separation of cooperative and non-cooperative games and the purpose of an “Ideal Money” creating transferable utility in a symmetric and independent system.
This could be the strongest game theoretically orientated explanation for the creation of Bitcoin because the “Nash program” regards all games or bargaining scenarios as non-cooperative, which may seem counter-intuitive to cooperative games as they’re considered more desirable or ideal since agreement points are easier to reach in the presence of collaborating players.
In a broader interpretation, the Nash program should be viewed as a framework to keep the dialogue between these two main branches of game theory open. The Nash program is sometimes regarded as “blurring the logic” in coalitional equilibrium concepts (1), and the reason for this is relatable to Bitcoin: the core mechanism of the Bitcoin system is self-enforcing but represents the axioms required for cooperative (or Nash) bargaining where cooperative bargains are externally enforceable by contracts or authorities like the police or courts. The reason for the “Nash program” is that cooperative games can be long-term difficult and costly to maintain (2) — e.g. see how the Bitcoin Whitepaper addresses the problem of all the trust required for traditional finance to work (3) — so that formalised external enforcement is removed because it’s believed only self-enforcing equilibrium (or non-cooperative) agreements are sustainable.
An example of this can be seen in John Nash’s Agencies Method for Modeling Coalitions and Cooperation in Games (4), where Nash uses the symmetry and independence axioms to explain market clearing of the resources allocated to players irrespective of the order of election of the players, just as the order of players or peers in the bitcoin system is irrelevant to the ongoing bitcoin block reward. This can be summarised as Bitcoin being an independent system unaffected by a third party (see how Nash references “two’s company, three’s a crowd” in Agencies), but potentially whose value could be recreated in something analogous to a final experiment of the Nash program and which might eventually become represented by simple and trusted human language in a readily translatable environment.
References.
- Sixty-seven years of the Nash program: time for retirement? Robert Serrano, 2020
- The Nash equilibrium: A perspective, Charles Holt & Alvin Roth, 2004
- Bitcoin: A Peer-to-Peer Electronic Cash System, Satoshi Nakamoto, 2008
- The Agencies Method for Modeling Coalitions and Cooperation in Games, John Nash, 2008
