Prisoner's Dilemma Fallacy

There is a theory that in a choice to join a ban on Bitcoin, individual states face a prisoner's dilemma. A meaningful ban implies one or more states (the "prison") will enforce economic sanctions (at least) on other states (the "prisoners") potentially moving to Bitcoin as a reserve currency.

We assume that the prisoners who may decide to use Bitcoin are trading partners. In other words the use of Bitcoin as a reserve currency is useful in that they have a partner with whom to transact.

The outcome for individual Bitcoin (Sucker):

• Economic sanction.
• An unusable reserve currency (no trading partners).

The outcome for mutual Bitcoin (Reward):

• Economic sanction.
• Trading partner economic sanction.
• A reserve currency not taxed via seigniorage.

The outcome for individual Dollar (Temptation):

• Inclusion in the global financial system.
• A reserve currency taxed via seigniorage.

The outcome for mutual Dollar (Punishment):

• Inclusion in the global financial system.
• A reserve currency taxed via seigniorage.

Payoff Matrix

Brazil\Ireland	Bitcoin	Dollar
Bitcoin	R\R	S\T
Dollar	T\S	P\P

T > R > P > S must be true, where:

• R > P implies that mutual Bitcoin is preferred by each to mutual Dollar.
• T > R and P > S imply that Dollar is the dominant strategy for each.

We can conclude that P > S holds, as individual sanction implies no international settlement and therefore no benefit from a foreign exchange reserve, and presumably economic sanctions are undesirable.

To determine if R > P and T > R, an objective measure is required to relate seigniorage and sanction. This can be obtained by the observation that Gold is subject to neither seigniorage nor sanction. In other words Gold provides the above benefits of Bitcoin without sanction. Yet Gold has not been chosen (and was previously dropped in favor of Dollar), which implies the Dollar outcome is preferred to Gold and therefore Bitcoin. As such, neither of the dominant strategies hold, invalidating the theory. The game does not represent a prisoner's dilemma.