Reserve Depletion and Security Runway in Proof-of-Stake Systems

Many proof-of-stake protocols finance validator rewards from two sources: transaction fees and a finite reserve of native tokens. This creates a dynamic hand-off problem. Early in the life of the system, fees may be too small to fund the target level of security; later, fees may become sufficient. The central question is whether the reserve provides enough runway for the protocol to remain secure until this fee-only region is reached. We study this problem in a discrete-time stochastic model of validator participation. Token price and transaction demand fluctuate over time, while validators choose participation strategically in each state. We solve the validator entry game in closed form and derive an exact state-dependent reserve threshold: for every token price and demand state, the threshold is the minimal reserve stock necessary and sufficient to sustain a target security level. This threshold separates three regions: infeasibility, reserve-dependent security, and fee-only security. The threshold turns reserve adequacy into a hitting-time problem. Security fails when the reserve first falls below the state-dependent threshold, and a successful hand-off occurs exactly when the fee-only region is reached before that failure time. We derive conservative finite-horizon stress-test guarantees that convert lower confidence bands for token price and demand into reserve requirements, and under lognormal price-demand dynamics we obtain explicit failure-probability and expected hand-off-time bounds. Finally, we extend the model to forward-looking validators and derive the Markov participation condition that captures how current participation affects future reserve-funded rewards. The main implication is that reserve policy should not be evaluated by nominal depletion dates or steady-state reward ratios alone. A protocol can have a large nominal reserve and still be close to security failure after adverse price or demand shocks. Conversely, once demand crosses the fee-only threshold, the reserve becomes redundant for security. This paper provides a tractable equilibrium framework for stress-testing this transition.