  All public blockchains are secured by a proof of opportunity cost among block
producers. For example, the security offered by proof-of-work (PoW) systems,
like Bitcoin, is due to spent computation; it is work precisely because it
cannot be performed for free. In general, more resources provably lost in
producing blocks yields more security for the blockchain. When two blockchains
share the same mechanism for providing opportunity cost, as is the case when
they share the same PoW algorithm, the two chains compete for resources from
block producers. Indeed, if there exists a liquid market between resource
types, then theoretically all blockchains will compete for resources. In this
paper, we show that there exists a resource allocation equilibrium between any
two blockchains, which is essentially driven by the fiat value of reward that
each chain offers in return for providing security. We go on to prove that this
equilibrium is singular and always achieved provided that block producers
behave in a greedy, but cautious fashion. The opposite is true when they are
overly greedy: resource allocation oscillates in extremes between the two
chains. We show that these results hold both in practice and in a block
generation simulation. Finally, we demonstrate several applications of this
theory including a trustless price-ratio oracle, increased security for
blockchains whose coins have lower fiat value, and a quantification of cost to
allocating resources away from the equilibrium.
