Lets try your system out...
Lets see if there is any merits to his thinking
That's what we are doing.
We are discussing his thinking, and demonstrating the shortcomings so that he (or anyone else) can consider possible solutions to those shortcomings.
One KNOWN solution is a proof-of-work blockchain. It has already been demonstrated to work VERY well in a small scale, and larger scale enhancements are being developed.
Another KNOWN solution is a centralized authority. It has already been demonstrated to work VERY well in a large scale, as long as the authority doesn't take advantage of their position or take actions that have a negative long term effect.
OP is suggesting that a Nash Equilibrium might be another solution. He or someone else is going to need to explain how that would provide a solution. As far as I'm aware, such a thing hasn't been attempted, and I've not heard anything about how it would solve the problem. At the moment it sounds a bit like asking: "Could you create some kind of a ham sandwich around hyperinflation caused by just allowing double spends?"
I'll openly admit I'm no expert on Nash Equilibrium, but just using the phrase Nash Equilibrium isn't going to solve a known problem.
given that Bitcoin needs fixing
That's off topic for this discussion. This isn't a discussion about efforts that are being made to "fix bitcoin". This is a discussion about an altcoin that would allow anyone to spend value that they don't have.
instead of being always on the attack.
Discussing problems with a concept which have not yet been addressed in a shared attempt to identify an unworkable concept or solve the problems in the concept is NOT "being on attack".
I like his way of thinking and when shop lifters get away with steeling then the cost gets past on to me and you
anyway
Correct. Which is why we have a centralized systems of authority: a shopkeeper, a police force, a lawmaking body, and a judicial body. If we want to rely on centralized systems of authority, then the existing systems of money are fine and there is no need to replace it with anything new.
Furthermore, this isn't about stealing, this is about counterfeiting. If "Bob" has 1 coin, and he can reproduce that 1 coin and spend his reproductions, then he has created counterfeit coins. The existing system of government currencies implements many features to make it difficult to counterfeit the currency. It also implements significant penalties for counterfeiting. The question being asked by the OP is "What if we just allowed everyone to create as much counterfeit government currency as they want to? Could we build some kind of Nash equilibrium around this?"
and two months ago Bob dare not send Alice a penny due to the $55 transaction fee but I bet you
have forgotten about that one now.
Nope. Haven't forgotten about it, but that's not relevant to this discussion.