the lower the F the higher the price. But in the ultimate equilibrium where there is no backlog, it is always and therefore .
Note that the price has only to do with the volume and energy power and irrelevant to many other characteristics of the cryptocurrency such as block time or transaction size. To generalize to a finite-volume cryptocurrency, its price is and its capital capacity is where V is its volume; die-hard holders (a coin holder who was dead or lost the keys) may increase the price but never the capital capacity.
Therefore, given this possibility that the energy power may switch among multiple cryptocurrencies, the best strategy to keep the whole wealth stable is to keep each currency position proportional to the currency volume . Denote the position of cryptocurrency i by :
which is irrelevant to the mining power distribution among these cryptocurrencies.
For forks of a cryptocurrency, this simply means doing nothing after the forks is the best strategy to keep wealth stable if one already holds a position before the fork and no ideas which fork would outwin at last. On the other hand, since a strong opinion about the failure of a specific fork is equivalent to a strong opinion that its energy power shall be zero, one can choose no position on that fork. Ironically, this reasoning also helps to decide the amount of position with fiat.
For merge of different cryptocurrencies, this simply means the coins amount after the merge shall be related to the total capital capacity. Denote:
Then it follows: