In many environments, a contest protects an activity whose revenue finances the contest: policing funded by property taxes, platform security funded by usage fees, insurance solvency funded by premiums. The prize is endogenous to the protection level. This article characterises the resulting fixed-point problem. Under primitive conditions on cost convexity, demand regularity, and attack technology, the equilibrium set forms a complete lattice with a shutdown state, a stable highsecurity equilibrium, and an unstable tipping threshold. Interior equilibria appear and vanish via saddle-node bifurcation, and all comparative statics inherit a common amplification denominator that diverges at the fold. The welfare-maximising fee lies below the revenue-maximising fee when the security externality is moderate. A continuous-time extension nests the static equilibria as stationary points.