Proof is in the article linked.

With the caveat that this 'proof' relies on the same assumptions that 'prove' that the rational prisoners defect in the one shot prisoners dilemma - which they don't unless they have insufficient (or inaccurate) information about each other. At a stretch we could force the "do not trust each other" premise to include "the pirates have terrible maps of each other" but that's not a realistic interpretation of the sentence. Really there is the additional implicit assumption "Oh, and all these pirates are agents that implement Causal Decision Theory".

Amazing, isn't it? :-)

It gets even more interesting when there are more than 200 pirates (and still only 100 coins).