Mind the Gap in the Mining Game

Battle Count: 59

The paper is primarily about blockchain mining economics and network stability rather than quantitative trading. However, it has indirect relevance: (1) mining gap dynamics affect Bitcoin's block generation timing and network security, which influence market microstructure; (2) transaction fee dynamics connect to on-chain congestion and fee estimation relevant for DeFi trading; (3) the halving mechanism and reward structure affect Bitcoin supply dynamics relevant to long-term asset allocation; (4) the game-theoretic framework could inform understanding of miner behavior during market stress. The connection to trading strategies is tenuous and indirect.

The analytical framework involves continuous-time differential games, Pontryagin's maximum principle, bang-bang optimal control, singular control analysis, and Nash equilibrium computation via recursive solution of switching function equations. The DAA stability analysis requires understanding of iterative map convergence. For the homogeneous affine case, closed-form solutions are tractable. However, general numerical implementation requires solving coupled optimal control problems, computing equilibrium start times recursively, and simulating DAA convergence. The Bitcoin calibration involves multiple data sources and parameter estimation.

The paper provides complete analytical proofs in the appendix, explicit closed-form solutions for the homogeneous affine case, and detailed numerical simulation parameters. However, no code repository is provided. Bitcoin network data is sourced from public platforms (mempool.observer, Cambridge Bitcoin Electricity Consumption Index). The two-player simulation parameters are fully specified, enabling replication of numerical results.