On the Profitability of Selfish Blockchain Mining Under Consideration of Ruin

Mining blocks on a blockchain equipped with a proof of work consensus protocol is well known to be resource consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining and is compensated by a capital gain when a block is discovered. This paper aims at quantifying the profitability of mining when the possible event of ruin is also considered. This is done by formulating a tractable stochastic model and using tools from applied probability and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when the miner withholds blocks. The obtained explicit expressions allow us to analyze the sensitivity with respect to the different model components and to identify conditions under which selfish mining is a strategic advantage.