A Difficulty in Controlling Blockchain Mining Costs via Cryptopuzzle Difficulty
This addresses a fundamental control issue in blockchain consensus protocols, but the result is negative and incremental, showing impossibility rather than a solution.
The paper tackles the problem of reducing mining costs in blockchain systems by modeling mining as an all-pay auction and investigating the design of a mining auction mechanism to induce a logit equilibrium with decreasing costs. It shows that no lenient allocation function can discourage miners from bidding higher costs under a bounded rate of change condition.
Blockchain systems often employ proof-of-work consensus protocols to validate and add transactions into hashchains. These protocols stimulate competition among miners in solving cryptopuzzles (e.g. SHA-256 hash computation in Bitcoin) in exchange for a monetary reward. Here, we model mining as an all-pay auction, where miners' computational efforts are interpreted as bids, and the allocation function is the probability of solving the cryptopuzzle in a single attempt with unit (normalized) computational capability. Such an allocation function captures how blockchain systems control the difficulty of the cryptopuzzle as a function of miners' computational abilities (bids). In an attempt to reduce mining costs, we investigate designing a mining auction mechanism which induces a logit equilibrium amongst the miners with choice distributions that are unilaterally decreasing with costs at each miner. We show it is impossible to design a lenient allocation function that does this. Specifically, we show that there exists no allocation function that discourages miners to bid higher costs at logit equilibrium, if the rate of change of difficulty with respect to each miner's cost is bounded by the inverse of the sum of costs at all the miners.