[p2p-research] Building Alliances

[J. Andrew Rogers]

On Fri, Nov 6, 2009 at 3:20 PM, Ryan Lanham <rlanham1963 at gmail.com> wrote:
> P2P theory is a mess...in a postmodern sense.
>
> The heat to light ratio is very high right now.  I'm personally looking for
> someone to emerge as the clear post-scarcity theorist.  Right now, it is
> muddled.  But maybe...  Every few days I think I can make some sense of
> it...but it slips away.  It is very difficult to get to a moral philosophy
> that aligns with a respectable futurism.


I did research a few years ago on the mathematics of optimally
efficient and pervasively decentralized networks. This theoretical
area is very important because it is used to prove all sorts of things
about cooperative systems of independent agents. It is literally the
mathematics of dynamics of P2P systems in the abstract and very
challenging theoretically with many unanswered questions. One thing
that has surprised me is that it is never discussed here even though
it is very relevant.

One of the critical theoretical problems of such systems is that there
are only two known strategies -- from two different theoretical
derivations -- for P2P system design that do not decay into
pathologically suboptimal equilibria. If you have a system that
necessarily cannot be constrained to those strategies, the system is
not stable in a well-functioning configuration.  The reason I was
researching it at all was because there was an interesting real-world
political policy problem that could not use either known strategy; I
never found a satisfactory solution, but I suspect one might not even
exist for that case.

The problem is that the two robust strategies in literature (someone
may have come up with a new one in the last couple years, probably
not) are both effectively based on adaptive market-like pricing
mechanisms. You can solve the problem with strong centralization, but
that has its own problems in real systems e.g. single point of
failure/corruption.

I don't have answers, but designing theoretically stable, strongly
decentralized P2P systems that do not have major provable pathologies
is very, very hard outside of some fairly narrow cases. I am very fond
of the idea of strongly decentralized P2P economies but I haven't seen
much in the way of a rigorous formulation of such a system here that
would be both robust and without significant pathologies.


-- 
J. Andrew Rogers
realityminer.blogspot.com