Research map / Multi-agent systems and games / Games and equilibria
Who’s Gaming the System? A Causally-Motivated Approach for Detecting Strategic Adaptation
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Frames agent gaming as utility maximization with a gaming deterrence parameter, shows it is only partially identifiable, and proves a ranking of agents by that parameter is recoverable via causal effect estimation over agent "treatments".
Problem
Identifying the agents (e.g., health insurance plans) that game an ML-guided decision most aggressively, without labels or known utility/cost functions, when the gaming parameter cannot be point-identified.
Approach
Introduces a gaming deterrence parameter lambda_p in a strategic-adaptation utility model; shows lambda_p is only partially identifiable (lower bound), but recasts ranking agents as pairwise causal effect estimation where each agent is a treatment, so the sign of the average treatment effect recovers the ranking of lambda_p.
Key results
- At 7 audits in synthetic data (high confounding), S+IPW reaches sensitivity 0.860 vs. 0.520 for KNN.
- Payout-only ranking performs worse than random under high confounding (AUSC 0.299 vs. 0.473).
- In the Medicare case study, S+IPW state rankings are positively correlated with the share of for-profit providers (e.g., OP PT/SP for-profit share, Spearman 0.294, p=0.036).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use S+IPW instead of KNN for agent ranking | Synthetic gaming detection · Synthetic data, mean range 0.9, 7 audits | top-5 sensitivity: 0.520±0.215 -> 0.860±0.135 | Helped |
| Use S+IPW instead of KNN for agent ranking | Synthetic gaming detection · Synthetic data, mean range 0.9, 7 audits | DCG: 42.3±10.8 -> 56.1±5.11 | Helped |
| Use S+IPW instead of KNN for agent ranking | Synthetic gaming detection · Synthetic data, mean range 0.0 | AUSC: 0.648±0.129 -> 0.614±0.096 | Hurt |
| Use payout-only ranking instead of random ranking | Synthetic gaming detection · Synthetic data, mean range 1.0 | AUSC: 0.473±0.101 -> 0.299±0.067 | Hurt |
| Increase confounding from mean range 0.0 to 1.0 | S+IPW · Synthetic data | AUSC: 0.614±0.096 -> 0.837±0.067 | Helped |
| Increase confounding from mean range 0.0 to 1.0 | DragonNet · Synthetic data | AUSC: 0.755±0.096 -> 0.696±0.083 | Hurt |
| Increase confounding from mean range 0.0 to 1.0 | R-learner · Synthetic data | AUSC: 0.728±0.114 -> 0.635±0.111 | Hurt |
| Rank states using S+IPW | Medicare state-level gaming detection · U.S. Medicare state rankings | Spearman correlation with for-profit provider prevalence: 0.294 | Helped |
Surprising findings
- A payout-only ranking can be worse than random when covariates confound agent decisions.
- S+IPW ranking performance improves as confounding increases.
Limitations
- Assumes agents always increase decisions and gaming explains all behavioral differences.
- Utility-maximizing behavior and conditional exchangeability are strong, statistically unverifiable assumptions.
- Medicare case study is exploratory; many correlations are not statistically significant and confounders such as care quality may explain results.
Experimental setup
Datasets: synthetic gaming data (generated) 2018-2019 U.S. Medicare claims 0.2% sample National Neighborhood Data Archive (NANDA) CMS Provider of Service files
Benchmarks: synthetic gaming data Medicare upcoding case study
Metrics: top-5 sensitivity at k DCG at k AUSC Spearman rank correlation
Baselines: payout-only ranking random ranking KNN outlier detection ECOD deep isolation forest PSM S-learner T-learner R-learner
Builds on: strategic classification Neyman-Rubin potential outcomes permutation weighting structured intervention network DragonNet
Closest papers by meaning
- Strategic Classification is Causal Modeling in Disguise (ICML 2020 · similarity 0.90)
- Causal Strategic Linear Regression (ICML 2020 · similarity 0.89)
- Causal Strategic Learning with Competitive Selection (AAAI 2024 · similarity 0.87)
- Understanding Model Selection for Learning in Strategic Environments (NeurIPS 2024 · similarity 0.86)
- Strategic Classification With Externalities (ICLR 2025 · similarity 0.86)
- Prediction-Intervention Games and Invariant Sets (NeurIPS 2026 · similarity 0.85)
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