The Stabilising Of Nash Equilibria In Bitcoin

By Jon Gulson on ALTCOIN MAGAZINE

John Forbes Nash Jr

It’s said if a clothing garment remains in a wardrobe long enough, it will come back into fashion. It’s similarly and also tiredly observed there may be nothing new under the sun.

Indeed, Nash equilibria is sometimes referred to as Cournot-Nash equilibria, which has become central to non-cooperative game theory, after French philosopher and mathematician Antoine Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly, and whose work is considered joined to John Nash (1928–2015) in the anticipation of no cooperation between rational bargain makers.

A question has also been raised on the extent of the similarity between Ludwig Wittgenstein (1889–1951) and his language game (sprachspiel) concept to the Nash equilibria: Nash thought it unnecessary to assume players have to go through complex reasoning to participate in a game, just as Wittgenstein regarded language usage more a casual and subconscious intuition.

Focal to Wittgenstein’s language game is the idea words and language don’t remain static over time. For example, the notion of volatility once referred to the light of movement and speed of direction, rather than stability threatening unpredictability:

The World Empire Context

To link Wittgenstein’s language game and the Nash equilibria, is to regard the creation and stabilisation of each as two parts of the same: when Bitcoin reached genesis, it created an equilibria between trustless (peer to peer) and trusted (mediated) money with central banks who engage in a forward guidance verbal oversight:

The decentralized nature of Bitcoin means it can’t be shepherded in such a fashion. Interestingly, when John Nash proposed a theoretical Ideal Money, he wrote his proposal wouldn’t be suitable for a world empire context.

And in considering a hypothetical scenario where Bitcoin were to sharply gain in value against the major fiat currencies, the cash creation required to sate Bitcoin demand would effectively converge the central banks toward a de facto Bitcoin standard: a world empire context begins to become a reality, changing the nature of Bitcoin’s decentralization.

The question becomes how much trustworthy money creation is enough?

The implications on the limits of Bitcoin are something Nash touched on:

The Renaissance Ideal

The limits of sovereign central bank multilateral agency in a world which is ever more interconnected might be causative of such a spark where Bitcoin gains against their issuance.

As the equilibria stabilize in this multilateral scenario, easier borders, and trusting agents may see a fervent rebirth of classical thinking similar to the Renaissance.

How the money and how the language evolve and create anew and how they entwine, is hard to say: the small casual transaction may become as casual as an intuition, just as Nash and Wittgenstein regarded complex reasoning unnecessary to know a game— and there may be nothing new under the sun in this regard, but it can’t stop our desire to bask in it.