Bitcoin Protocol Analysis: Game Theory and Protocol Integrity

This thesis develops a unified mathematical framework for analysing the economic dynamics of proof-of-work mining in scalable digital cash systems. The central contribution is the construction of an unbounded-horizon stochastic game that embeds the full mechanical structure of proof-of-work—hashing, block construction, fee formation, difficulty retargeting, propagation conditions, and validation constraints—into a coherent optimisation environment in which miners act strategically across time. The model shows that miner behaviour, protocol-consistent action, concentration patterns, and the observed cyclicality of hash rate and difficulty arise endogenously from the interaction between dynamic incentives and protocol mechanics rather than from static or heuristic assumptions. The analysis establishes a formal link between block-production probabilities, state-dependent revenue surfaces, variable and structural costs, and transition dynamics driven by fee density and lagged difficulty adjustment. The resulting value functions generate state-contingent policy rules that produce the characteristic sawtooth patterns seen in empirical hash-rate data, demonstrating that these cycles are equilibrium objects rather than irregularities. The framework identifies the conditions under which protocol-compliant behaviour is a best response over unbounded horizons and explains how scale economies in transaction validation, template management, and propagation yield the endogenous emergence of large mining entities. The thesis integrates formal modelling, comparative statics, and simulation to show how miner incentives evolve as systems transition to fee-dominated environments and high transaction throughput. The framework provides a rigorous basis for evaluating protocol-level design choices, their impact on long-run incentives, and the equilibrium stability of scalable proof-of-work systems.<p></p>

Author dc:creator

• Craig Wright (21040430)

• Proof-of-Work
• Mining Economics
• Dynamic Games
• Markov-Perfect Equilibrium
• Difficulty Adjustment
• Fee Dynamics
• High-Throughput Digital Cash Systems
• Contest Theory
• Strategic Optimisation
• Protocol Compliance

Statement dc:rights

• All rights reserved

Identifier

10779/exe.31454308.v1

OAI identifier oai:identifier

oai:figshare.com:article/31454308