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.
Mining is a central operation of all proof-of-work (PoW) based cryptocurrencies. The vast majority of miners today participate in "mining pools" instead of "solo mining" in order to lower risk and achieve a more steady income. However, this rise of participation in mining pools negatively affects the decentralization levels of most cryptocurrencies. In this work, we look into mining pools from the point of view of a miner: We present an analytical model and implement a computational tool that allows miners to optimally distribute their computational power over multiple pools and PoW cryptocurrencies (i.e. build a mining portfolio), taking into account their risk aversion levels. Our tool allows miners to maximize their risk-adjusted earnings by diversifying across multiple mining pools which enhances PoW decentralization. Finally, we run an experiment in Bitcoin historical data and demonstrate that a miner diversifying over multiple pools, as instructed by our model tool, receives a higher overall Sharpe ratio (i.e. average excess reward over its standard deviation volatility). The rise of centralized mining pools for risk sharing does not necessarily undermine the decentralization required for public blockchains. However, mining pools as a financial innovation significantly escalates the arms race among competing miners and thus increases the energy consumption of proof-of-work-based blockchains. Each individual miner's cross-pool diversification and endogenous fees charged by pools generally sustain decentralization --- larger pools better internalize their externality on global hash rates, charge higher fees, attract disproportionately fewer miners, and thus grow slower. Empirical evidence from Bitcoin mining supports our model predictions, and the economic insights apply to many other blockchain protocols, as well as mainstream industries with similar characteristics. Abrupt changes in the miner hash rate applied to a proof-of-work (PoW) blockchain can adversely affect user experience and security. Because different PoW blockchains often share hashing algorithms, miners face a complex choice in deciding how to allocate their hash power among chains. We present an economic model that leverages Modern Portfolio Theory to predict a miner’s allocation over time using price data and inferred risk tolerance. The model matches actual allocations with mean absolute error within 20 for four out of the top five miners active on both Bitcoin (BTC) and Bitcoin Cash (BCH) blockchains. A model of aggregate allocation across those four miners shows excellent agreement in magnitude with the actual aggregate as well a correlation coefficient of 0.649. The accuracy of the aggregate allocation model is also sufficient to explain major historical changes in inter-block time (IBT) for BCH. Because estimates of miner risk are not time-dependent and our model is otherwise price-driven, we are able to use it to anticipate the effect of a major price shock on hash allocation and IBT in the BCH blockchain. Using a Monte Carlo simulation, we show that, despite mitigation by the new difficulty adjustment algorithm, a price drop of 50 could increase the IBT by 50 for at least a day, with a peak delay of 100 .