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All public blockchains are secured by a proof of opportunity cost among blockproducers. For example, the security offered by proof-of-work (PoW) systems,like Bitcoin, is due to spent computation; it is work precisely because itcannot be performed for free. In general, more resources provably lost inproducing blocks yields more security for the blockchain. When two blockchainsshare the same mechanism for providing opportunity cost, as is the case whenthey share the same PoW algorithm, the two chains compete for resources fromblock producers. Indeed, if there exists a liquid market between resourcetypes, then theoretically all blockchains will compete for resources. In thispaper, we show that there exists a resource allocation equilibrium between anytwo blockchains, which is essentially driven by the fiat value of reward thateach chain offers in return for providing security. We go on to prove that thisequilibrium is singular and always achieved provided that block producersbehave in a greedy, but cautious fashion. The opposite is true when they areoverly greedy: resource allocation oscillates in extremes between the twochains. We show that these results hold both in practice and in a blockgeneration simulation. Finally, we demonstrate several applications of thistheory including a trustless price-ratio oracle, increased security forblockchains whose coins have lower fiat value, and a quantification of cost toallocating resources away from the equilibrium.

Greedy but Cautious: Conditions for Miner Convergence to Resource Allocation Equilibrium