Coordinating security investment in the authorized operation of public data: a tripartite evolutionary game analysis

Authorized public-data operation links source-data preparation by public-sector providers, secure product and service development by authorized operators, and security supervision by regulators. These actors face interdependent investment decisions, because the safeguards provided by one party can benefit the other while additional governance investment remains costly. This paper develops a tripartite evolutionary game in which providers choose between additional source-data governance and baseline compliance, operators choose between additional platform and downstream governance and baseline operation, and regulators choose between enhanced and routine oversight. The payoff structure integrates bidirectional free-riding, unilateral and joint investment returns, and behavior-contingent regulation, with actor-specific returns, costs, policy support, expected liabilities, accountability losses, and deterrence value represented separately. From the resulting payoff differences, the analysis derives closed-form investment and regulatory thresholds and exact local-stability conditions for the eight pure-strategy states. Coordinated investment is locally stable only when both operating parties obtain positive net returns from joint investment. One-sided return deficits therefore sustain one-sided investment outcomes even when the other party invests or enhanced oversight remains active. In the benchmark, the all-invest, enhanced-oversight state is unstable, whereas mutual investment combined with routine, risk-based oversight can be stable. Normalized numerical experiments illustrate the seven potentially stable vertex configurations under selected parameter regimes and examine initial conditions, revenue sharing, regulatory cost, and symmetric deterministic exploration. The results indicate when actor-specific incentives, joint-return allocation, and behavior-contingent accountability can sustain coordinated investment and permit a transition from enhanced intervention to routine oversight. The numerical results are presented on a dimensionless scale and support mechanism-level comparisons across threshold regions.