http://steemit.com/steemit/@r0achtheunsavory/the-r0ach-report-14-defining-if-cryptocurrency-has-a-value-or-zero-value-from-a-fundamental-scientific-perspective
It's relatively short to read, but if you want the TLDR version, my stance is that proof of stake has no value whatsoever and I explain why, and proof of work with ASIC is almost functionally the same thing (externalized proof of stake) in practice and would also have no value. I don't think anyone will find a valid argument against this post.
I don't care for Proof of Stake so no argument from me on that. However, I disagree with your assumptions regarding Proof of Work.
This is a big centralization pressure, but arguably not a terminal one if you believe the energy costs on the planet are not outrageously lopsided in uniformity. The next evolution of the system was the introduction of ASIC mining. This is yet another layer of centralization on top of energy costs which I believe is not just additive, but more like multiplicative or quadratic in nature with the previous layer. Now your matrix of miners tends to look something like this instead:
It's a completely arbitrary number, but once you've reached a point where you can fit all the actors together into a large car where they can collude and form an OPEC-style cartel, doing things like blocking transactions from people they don't like, setting transaction fees abnormally high, or forking the network, you obviously no longer have any form of Nash equilibrium and the system I would say has become inherently valueless. No, this does not magically mean proof of stake now has value; it never had value in the first place.
What you fail to consider is that theoretical cartel actors cannot actually do any of these things in a profitable manner. Bitcoin is a consensus system. Unlike fiat its use is not enforced by state authority and violence. It requires the voluntary participation of each individual transacting in it.
Leaders in the bitcoin community have an economic incentive to behave above board. If they do not users will simply leave converting their bitcoins to something else that is managed better. This may happen through a fork of an outraged minority or people simply leaving for another coin.
Bitcoin's dominance is not guaranteed going forward. It will retain its position and value only if its community members behave in the manner necessary to maintain a broad consensus. Shatter the consensus be it via a community fracture, or mining cartel and all bets are off.
Nash equilibrium is enforced despite the existence of powerful actors by the free mobility of capital into and out of the currency in response to divergences away from the stable state.