My understanding of Nash's mathematical theory of ideal money is that if we have unit-of-account and store-of-value for reserves (but not necessarily a medium-of-exchange!) which has a non-manipulable and predictable rate of change of its supply, then that money can form the basis of sound financial systems which correctly value the activities in the economy and thus don't create distortions which lead to for example the failure of private fractional reserve banking, depressions, and misallocation of economic resources and capital.
So this is why the primary value of Bitcoin is the inability to change its protocol. If Bitcoin's protocol can be changed by anyone, then it is no longer a reliable metric in Nash's mathematical scheme.
So Satoshi tried to design a monetary system which would meet the requirements of Nash's ideal money scheme. Because in theory this can bring great benefits to society, such as destroying all the fiat systems, corrupt governments and destroying the inherently correct concept of socialism and democracy. These justifications have been explained in more detail upthread (and in extensive detail in my archives on BCT), so I won't repeat that information.
But as I already explained upthread, the immutability of PoW only exists for the token (blockchain) which has the greatest value, because the finance tail doesn't wag the dog. I explained upthread that whales on a higher valued blockchain can potentially manipulate a lowered valued altcoin as is the case ongoing now with Litecoin wherein they are able to change the protocol.
I also explained upthread how (using MPEx as an example) finance always accumulates to the one with the most reserves, i.e. finance is inherently a winner-take-all construct. It is a gravitational system that sucks everything into itself until it is the entire economy and then it self-destructs. Thus Nash's ideal money can't exist in reality with finance.
Nash wanted an asymptotic solution wherein the number of stable currencies could be unbounded and thus no one could ever gain sufficient omniscient information in order to winner-take-all the financial system. Unfortunately Bitcoin as the center of the financial universe as the only
stable currency is of course an abomination and not at all what Nash would have wanted. (Note altcoins are not stable currencies because they are not immutable.) Because of course I explained already upthread how over time there will end up with one whale who has monopolized the Bitcoin economy and thus can change the protocol at-will. This is why I say Bitcoin is the NWO system and was probably created by a think tank funded by an elite globalist such as Rothschild.
Nash required two incongruent things. He wanted a metric to be stable so the (rest of the) financial system could be measured against it, yet he also needed that metric to be absolute (as in its veracity/protocol not being relative to anything which could be controlled or gamed). There are no absolutes in our universe. We live in a relativistic universe which is only constructed from relative perspectives. None of us can even communicate our present to everyone and we can't even communicate our histories incontrovertibly because there is no way to prove an event happened other than by the corroboration of the memories of others who witnessed it (which is not a total ordering thus isn't incontrovertible). For example (but this is by no means the main point of what I am trying to explain here), this weakness in fungible money is why money requires a total ordering consensus so as to order the transactions globally to insure a double-spend wasn't attempted some where else in the universe.
I wrote as @anonymous:
O/T assigned a descriptive model where nodes or their connections are assumed to have unequal value without any model for why they do. Eric posited a generative model wherein communication has a space-time frictional cost. Subsequent commentary has pointed out that the more generalized generative model is that networking (in the generalized conceptualization of communication and/or group formation) has a myriad of genres of opportunity cost (e.g. even political opportunity cost in cooperative games theory), so this can account for preferences in group formation which may in some cases be independent of physical transport costs.
Something else occurred to me while reading the O/T paper before reading Robert Willis's thoughts, and I think combining the opportunity cost generalization with the following insight might model his point. Note that if the possible connections between nodes are limited by opportunity cost weighted compatibility of groups of nodes, then we can approximate a model of the network as connections between groups (aka clusters) of nodes. In this case, the equations for relative value of network mergers changes such that it is possible for the value proposition to invert between small and larger networks, if the larger network has fewer groupings (on an opportunity cost potential connections weighted basis). O/T mentioned clusters but in the context of their descriptive model of assumed unequal value. The key point of opportunity cost is that value is relativistic to the observer. The highly relativistic model is capable of higher-order effects such as those described by Robert Willis. Demographics matter.
I want to investigate whether Verlinde's entropic force
emergent information based gravitation model is applicable and perhaps a generative mathematical foundation.
So I believe what Nash worked out in his mind mathematically was that in some hypothetical asymptotic case wherein there are an unbounded number of stable, non-manipulable currencies, then it would not be possible for any player in the system to always win just because he/she held the most reserves, because that player would lack information about whether he/she held the most powerful basket of reserves, so it would thus not be a power vacuum winner-take-all outcome in the theoretical asymptotic case. So Nash was correct that in the asymptotic case, his ideal money is stable, but the problem is that such an asymptotic case isn't known to exist nor does anyone know how to make it come into existence. Even Satoshi's design requires Bitcoin to be the stable currency with the highest value otherwise as I had explained, its immutability is not assured by the game theory.
Precisely four years ago, I wrote
Bitcoin : The Digital Kill Switch, and I see now that I was entirely correct. Bitcoin is an abomination of Nash's ideal money scheme. Its end game is one globalist who controls everything. One omnipotent whale who stomps on all life. The NWO-666 outcome. Sorry I can't stand by idle and let that happen! Four years ago, I set out to try to figure out how to fix this problem. I've been working incessantly ever since on this in spite of my disseminated Tuberculosis illness (which I am now undergoing treatment to cure hopefully).
But along my journey of thinking about money every since I got interested in gold in 2006 because by late 2005 I could already see in my mind that a global crisis of debt and socialism was ahead in the real world, I ended up making a discovery and writing it down some time in the period between 2011 and 2013. That essay was
Rise of Knowledge, Demise of Finance.
The generative essence of that discovery was that knowledge can't be financed, because unlike manual labor, knowledge production is not fungible. Read the essay I wrote for more explanation.
Also Eric S. Raymond had discovered Linus' Law "
given enough eyeballs, all bugs are shallow" when he wrote the seminal
The Cathedral and the Bazaar which launched the open source revolution and Eric had invented the term "open source" preferring it over Richard Stallman's "free software". Eric followed that up with the explanation of open source economics models in the
Magic Cauldron wherein he explained the opposite of a Tragedy-of-the-Commons is an
Inverse Commons which is what open source is.
So what I had figured out that finance would die because the entire point of money is an information system which routes perception of value to those who help the society produce the most. Fungible money worked during the tangible ages (agriculture and industrial) because society needed to aggregate large amounts of capital (because economies-of-scale were paramount in agriculture and industry) and labor was fungible (i.e. replaceable) and thus finance was useful for maximizing production. Companies aggregate fungible resources and economies-of-scale to gain
a transactional cost advantage to solve the coordination problem of the Tragedy-of-the-Commons of uncoordinated resources per the Theory of the Firm (and such transactional cost advantages decline in the knowledge age due to technological changes which enable more diverse production with lower economies-of-scale and Inverse Commons coordination). Although this system carried with it huge social problems because laborers had no pricing power unless they could restrict membership (e.g. unions) or otherwise use the government to try to redistribute wealth (or do birth control eugenics to lower their competition with each other). In other words, the broken concepts such as democracy and socialism were ramifications of the fact that labor was too fungible (replaceable) and finance was cardinal. That is why so many hate capitalism, but they don't understand that the fledgling knowledge age (which is already underway!) will change everything to a meritocracy and destroy finance and money.
So we tie all this together and note that we increasingly are exchanging our knowledge and doing knowledge creation in open source Inverse Commons, especially those who produce the most in the new economy of the knowledge age. Eric Raymond had eloquently pointed out that the Inverse Commons of open source is the only known positive scaling law of engineering. And it applies to almost any field of knowledge creation that applies the open source principle (such as what we doing right now here by discussing a new concept and peer reviewing it here).
So I figured out that if I could tie the knowledge production within Inverse Commons to exchange of a fungible monetary unit, I could bridge the gap between where we are now and where we are headed. And that each time some fungible money would be exchanged in this system I designed, then the value of the fungible money would not be in exchange for the knowledge but rather in exchange for the service provided to host the knowledge. Then the fungible portion of exchange would only be a small fraction of the non-fungible value created by the activity. This was a very clever and insightful and essential discovery that I made!
So I had figured out a way to make new blockchain currency which would scale out larger than Bitcoin and thus defeat it while also itself not being vulnerable to manipulation because the fungible finance portion of the economy would orders-of-magnitude inferior in relative value to the knowledge portion. In other words, no one could ever monopolize it.
Then I combined that with a clever consensus algorithm which doesn't require PoW. And voila I named the unpublished design the Bitcoin Killer.
In other words, it achieves Nash's asymptotic ideal money by turning a person's brain into their non-fungible money (the unbounded number of brains is the asymptotic domain) and leverages that huge value creation in order to make the associated fungible token more demanded than Bitcoin. The economy shifts from a predominately monetary one into a predominately reputation and gift culture, wherein we recognize value by accomplishments and not by monetary digits.
Those parasite high finance and Wallstreet thugs have to find a new vocation and actually work together in society or become irrelevant.
I rather like my discovery. I think you will too if I am correct.
Bitcoin most probably won't exist any more then.