Hello all,

I've created a simulator for Bitcoin mining which goes a bit further than
the one Gavin used for his blog post a while ago. The main difference is
support for links with different latency and bandwidth, because of the
clustered configuration described below. In addition, it supports different
block sizes, takes fees into account, does difficulty adjustments, and
takes processing and mining delays into account. It also simulates longer
periods of time, and averages the result of many simulations running in
parallel until the variance on the result is low enough.

The code is here: https://github.com/sipa/bitcoin-net-simul

The configuration used in the code right now simulates two groups of miners
(one 80%=25%+25%+30%, one 20%=5%+5%+5%+5%), which are well-connected
internally, but are only connected to each other through a slow 2 Mbit/s

Here are some results.

This shows how the group of smaller miners loses around 8% of their
relative income (if they create larger blocks, their loss percentage goes
up slightly further):

  * Miner group 0: 80.000000% hashrate, blocksize 20000000.000000
  * Miner group 1: 20.000000% hashrate, blocksize 1000000.000000
  * Expected average block size: 16200000.000000
  * Average fee per block: 0.250000
  * Fee per byte: 0.0000000154
  * Miner group 0: 81.648985% income (factor 1.020612 with hashrate)
  * Miner group 1: 18.351015% income (factor 0.917551 with hashrate)

When fees become more important however, and half of a block's income is
due to fees, the effect becomes even stronger (a 15% loss), and the optimal
way to compete for small miners is to create larger blocks as well (smaller
blocks for them result in even less income):

  * Miner group 0: 80.000000% hashrate, blocksize 20000000.000000
  * Miner group 1: 20.000000% hashrate, blocksize 20000000.000000
  * Expected average block size: 20000000.000000
  * Average fee per block: 25.000000
  * Fee per byte: 0.0000012500
  * Miner group 0: 83.063545% income (factor 1.038294 with hashrate)
  * Miner group 1: 16.936455% income (factor 0.846823 with hashrate)

The simulator is not perfect. It doesn't take into account that multiple
blocks/relays can compete for the same bandwidth, or that nodes cannot
process multiple blocks at once.

The numbers used may be unrealistic, and I don't mean this as a prediction
for real-world events. However, it does very clearly show the effects of
larger blocks on centralization pressure of the system. Note that this also
does not make any assumption of destructive behavior on the network - just
simple profit maximalization.

Lastly, the code may be buggy; I only did some small sanity tests with
simple networks.

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