This is exactly why Satoshi cannot be Nash.  Satoshi's creation contains too many blunders (mathematical, cryptographic, economical, game-theoretical and programmatic) to be made by a genius like Nash.  Contrary to what many in the bitcoin world believe, Satoshi wasn't a genius at all (or he was a very evil one hiding what he was really up to).  Satoshi DID have some bright ideas.  And he also did mess up quite a bit, and as such, he did demonstrate he didn't deeply understand certain aspects of what he was doing.  Nash can't be that silly.  Or his high age had deteriorated his genius.

I already indicated several of these silly errors in bitcoin.  One more: the true protection of a bitcoin signature is NOT the elliptic signature scheme, but rather the hash function that transforms the public key into an address.  If a bitcoin address is only used once, the cryptographic security of the digital signature scheme doesn't need to be strong at all.  There's no need to go to 256 bit elliptic curve signatures: in fact the signature scheme only needs to withstand attacks during the time the transaction is broadcast, and is included in the block chain: so at most an hour or so (unless full blocks ) and even 10 minutes is good enough.

The reason is that the public key is only made public when signing a transaction.  Even a very cheap signature scheme would be good enough: it will withstand 10 minutes to an hour.  The public key is invisible as long as the hash function is secure.  I said somewhere else that it was totally utterly stupid to have 256 bit signatures but only a 160 bit hash.  But the complexity of the elliptic curve signature scheme was total overkill.  A genius like Nash would not even be capable of thinking of such a blunder.

Satoshi did have bright insights, he wasn't an idiot.  But he wasn't a genius (I see a genius as someone with very profound, deep insight in matters that nobody was understanding at that point).  

This is often a confusion: people think that "successful" people are genius.  Genius is rarely successful, because the deep insight also shows the genius all the limitations of a possible creation, refraining him from going ahead.  A successful person has a bright idea with limited understanding, over-estimates his view on things, and hence doesn't realize that his creation has serious flaws.  This allows him to focus all his energy on his half-failed idea, which, with sufficient luck, becomes a temporary success.

This is also why the elite is not very bright, but has had some successful ideas and mainly a lot of luck.  It is why they are arrogant, and mess up things: because of their limited understanding of things, and their confusion between the fact that they were just lucky to be successful, thinking erroneously that it is caused by their "genius" they are in fact totally lacking.

The successful elite are lottery winners that think that they know better than anyone else how to win at lotteries.  True genius is not like that.  Satoshi has made a successful invention with a lot of profound errors (like most successful things), because he had some bright ideas and was totally lacking the profound insight of the system he had created - lack of insight which allowed him to persevere in his creation of bitcoin.