The Nash Equilibrium in Digital Cash Systems: Revisiting Rational Choice Under Transaction Validation Constraints

This article examines Nash equilibrium stability in digital cash systems, using Bitcoin as a canonical model for protocol-constrained strategic interaction. Building on the formal framework established in Wright (2025), we characterise mining as a repeated non-cooperative game under endogenous constraints: hashpower allocation, latency asymmetries, fee-substitution dynamics, and institutional noise. We show that equilibrium behaviours are sensitive to the structural composition of miner rewards—specifically, the transition from subsidy-dominated to fee-dominated environments—and that volatility in protocol rules leads to equilibrium multiplicity and eventual collapse. Using tools from mainstream game theory and Austrian time preference theory, we demonstrate that rational strategic cooperation is only sustainable under strict protocol immutability. Rule mutation introduces uncertainty that distorts intertemporal valuation and incentivises short-term extractive strategies. These results suggest that digital monetary systems must be governed by non-negotiable constitutional rules to preserve incentive compatibility across time.