Zero Sum Property

Bitcoin mining is a zero sum game. On average the chain grows by one block every 10 minutes, with the full reward controlled by its miner. Miners compete to achieve this reward and will, apart from pooling pressures, each average a number of rewards proportional to hash power. The difference between a miner's cost and this reward over time is the rate of return on capital invested in the mine.

There are two aspects of the zero sum property:

• For the time period between organizations one miner earns a reward and all other miners earn no reward. Neither price, hash rate, difficulty, inflation, fees, nor anything else has any effect on this property.

• The magnitude of rewards, in either coin units or exchange price, has no effect on the rate of return on capital.

Idealized Bitcoin mining is a closed system. Return on capital does vary relative to other mines, due to the proximity premium and variance discount protocol flaws, as well as economies of scale and operator efficiency. Yet because these only impact the relative cost of hash power, the proportionality of return rates is affected, not overall returns.

Actual Bitcoin is not a closed system. The market and anti-market pooling pressures of variation and distortion (respectively) are external. Fundamentally Bitcoin exists to defend markets, necessarily pitting distortion against variation (or lack thereof).

When a distortion is applied to a miner in this zero sum system, all other miners are affected. For example, a subsidy to one miner acts as a tax on all others, and a tax on one miner acts as a subsidy to all others. The subsidized miner operates at a lower cost for the same hash rate, or has a higher effective hash rate for the same cost. The taxed miner operates at a higher cost for the same hash rate, or has a lower effective hash rate for the same cost.

A subsidizer expects no return on capital, otherwise he/she would be an investor. Investment is a market force whereby the miner pays a market price for capital. With a higher effective rate of return the subsidized miner attracts more capital than other miners, continuing to expand hash power until there is only one miner. The subsidizer's objective is ultimately control over the subsidized mine.

A tax on mining has the effect of moving all hash power to untaxed mines, presumably beyond the reach of the taxing authority, as capital seeks market returns. If applied broadly, this can give the authority control through its own mining operation. In other words, the authority can suppress competition. This can also be accomplished through a 100% tax, whereby the authority simply seizes existing mines and then starts operating them. The effect is the same, the taxed miner is put out of business, and the proceeds of the tax are applied to control.

The only way to defeat subsidy is to mine at a capital loss, either in absolute terms or relative to market return on capital (opportunity cost). The only way to defeat tax, up to and including a 100% tax/ban, is to mine in secret. As with all black markets there is an increased cost to subversive mining. Competing against subsidized mining compounds the cost.

If one considers states a threat to hard currency one must assume that both tax and subsidy will be used to reduce the cost of achieving control over Bitcoin. In order to enjoy the benefits of a hard currency, people will ultimately have to mine at a loss. However states will need to incur the same loss in order to continue to extract that loss. This is economic model of market aggression pitted against free markets.