Evaluating AI Investment Strategies

Fraud can pose a challenge in many resource allocation domains, including social service delivery and credit provision. For example, agents may misreport private information in order to gain benefits or access to credit. To mitigate this, a principal can design strategic audits to verify claims and penalize misreporting. In this paper, we introduce a general model of audit policy design as a principal-agent game with multiple agents, where the principal commits to an audit policy, and agents collectively choose an equilibrium that minimizes the principal's utility. We examine both adaptive and non-adaptive settings, depending on whether the principal's policy can be responsive to the distribution of agent reports. Our work provides efficient algorithms for computing optimal audit policies in both settings and extends these results to a setting with limited audit budgets.

Continuous post-deployment compliance audits, mandated by emerging regulations such as the EU AI Act and Digital Services Act, create a class of strategic gaming distinct from the one-shot input/output gaming studied in prior work. Regulated systems can delay outcome reporting, drift their reports within plausible noise envelopes, exploit longitudinal sample attrition, and cherry-pick among ambiguous metric definitions. We formalize continuous auditing as a $T$-round Stackelberg game between an auditor that commits to a temporal policy and an adaptive auditee, and identify a structural feature of any noise-aware static-auditor design: a cover regime in which coverage gaps and granularity gaps cannot be closed simultaneously. We make this formal as Observation 1 and show that two minimal extension policies, each derived from the observation, close the regime along orthogonal axes: a sample-size-aware static rule (Periodic-with-floor) closes the granularity-failure case, while a history-conditioned suspicion-escalation policy closes the coverage-failure case for the naive Drift strategy -- and neither closes both, exactly as the observation predicts; an audit-aware OffAuditDrift strategy that exploits Stackelberg commitment defeats both. To support empirical study we contribute a non-additive harm decomposition (welfare loss $W$, coverage loss $C$) that exposes how attrition shifts harm from the regulator-accountable surface to a regulator-invisible one; an initial library of five auditee strategies (Delay, Drift, Cherry-pick, Attrition, OffAuditDrift) and five auditor policies, calibrated to summary statistics from published audits of the DSA Transparency Database; and a reproducible simulator with a small, extensible Python interface.

Regulatory audits of AI systems increasingly rely on differential privacy (DP) to protect training data and model internals. We study audit design when the audited developer can strategically respond to the privacy-constrained audit interface. We formalize privacy-constrained auditing as a bilevel Stackelberg game, in which an auditor commits to a query policy and DP budget allocation across harm dimensions, and a strategic developer reallocates mitigation efforts in response. We introduce the welfare-weighted under-detection gap $B_w$, the welfare-weighted true residual harm the audit fails to detect at the developer's strategic best response, and prove that naive DP auditing (uniform or harm-proportional allocation) induces a strictly larger $B_w$ than any non-strategic mitigation baseline whenever effective detectability is heterogeneous, the welfare weights are not comonotone with detectability, and the developer's optimum is interior. We characterize the optimal auditor allocation as a four-factor balance of welfare weight, audit miss-probability, detectability elasticity, and mitigation-cost curvature, and provide a single-level reformulation of the bilevel problem via the developer's KKT system. We propose Strategic Private Audit Design (SPAD), a projected-gradient algorithm with hypergradients computed through the developer's best response.