I’d like to nail things down about the very dangerous monopoly
Suppose that we have k saturated pools with 10% pledge. How a new pool could compete with them?
Well at the very beginning a new pool will start only with pledge and no delegators so its reward formula will be f(s, σ) = R / (1+a0) * ( s’ + a0 * s’^3/z0^2 )
Now to attract delegators he will need to compete in the first place with the RoS of the k saturated pools. The reward formula for those pools is f(s, σ) = R / (1+a0) * ( zo + a0 * z0 / 10 )
Therefore to start competing in term of RoS the new will will need to have s’^2/z0^2=1/10 that is s’= z / sqrt(10) = z/ 3.16.
Therefore a new pool will need to invest a pledge almost 3 times superior than already established pools to start compete with them in terms of RoS and attract delegators, (then he will be able to lower it’s pledge as he gets delegators).
At this point it seems to me that it starts to be hard for anyone to argue that this formula is viable in any way.