"However, that is outside the scope of the result that an individual miner's profit per block is always maximized at a finite block size Q* if Shannon Entropy about each transaction is communicated during the block solution announcement. This result is important because it explains how a minimum fee density exists and it shows how miners cannot create enormous spam blocks for "no cost," for example. "

Dear Peter,

This might very well not be the case. Since the expected revenue <V> in our formulas is but a lower bound to the true expected revenue, and the fee supply curve $M_s(Q)\propto 1/\langle V\rangle$ , if the true expected revenue doesn't decay faster than the mempool's average transaction fee (or, more simply, if it doesn't decay to zero) then the maximum miner surplus will be unbounded and unhealthy fee markets will emerge.

Best,

Daniele

Daniele Pinna, Ph.D

On Sun, Aug 30, 2015 at 10:08 PM, Peter R <peter_r@gmx.com> wrote:

Hi Daniele,

I don't think there is any contention over the idea that miners that control a larger percentage of the hash rate, h / H, have a profitability advantage if you hold all the other variables of the miner's profit equation constant. I think this is important: it is a centralizing factor similar to other economies of scale.

However, that is outside the scope of the result that an individual miner's profit per block is always maximized at a finite block size Q* if Shannon Entropy about each transaction is communicated during the block solution announcement. This result is important because it explains how a minimum fee density exists and it shows how miners cannot create enormous spam blocks for "no cost," for example.

Best regards,
Peter

2) Whether it's truly possible for a miner's marginal profit per unit of hash to decrease with increasing hashrate in some parametric regime.This however directly contradicts the assumption that an optimal hashrate exists beyond which the revenue per unit of hash v' < v if h' > h.
Q.E.D

This theorem in turn implies the following corollary:

COROLLARY: The marginal profit curve is a monotonically increasing of miner hashrate.

This simple theorem, suggested implicitly by Gmaxwell disproves any and all conclusions of my work. Most importantly, centralization pressures will always be present.