Hi all,

it's a very useful approach to also model fees and you came up with an 
interesting scenario.
Assuming that you meant that the groups are only connected with a single link,
I've recreated the scenario with Gavin's simulation and got similar results.
The group with the large hashrate does profit overall, but the miners which are 
not directly
connected to the small group loose:

Moreover, it's important to note that this is not an equilibrium because these 
miners are better off when they create their own
connections to the small group (see the plot below the other one).
This means that your scenario is not the result of a cartel but the result of a 
long-term network partition.
When assuming partitions, there are quite a few scenarios where big miners can 
profit from creating big
blocks. For example, one 40% miner and two groups of three 10% miners, where 
both groups are connected to the big
miner but they are not connected to each other.


On 06/12/2015 06:51 PM, Pieter Wuille wrote:
> 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
> link.
> 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):
> Configuration:
>   * 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
> Result:
>   * 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):
> Configuration:
>   * 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
> Result:
>   * 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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