REVIEW 3 major objections 4 minor 4 cited by
Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty
T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash
Pith's one-line read A linear classifier steers strategic agents' effort toward desirable features exactly when those features win the contribution-per-cost ranking; uncertainty then turns optimal effort into a mean–variance tradeoff that avoids high-variance…
desk verdict The complete-information results are clean and worth keeping; the incomplete-information section rests on a false Gaussianity claim that leaves the paper's main advertised tractability results unsupported. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the contribution matrix $C = \sum_{k=0}^{|F|} A^k$ of the acyclic causal graph, whose entry $C_{ij}$ sums the products of edge weights over all directed paths from feature $i$ to feature $j$; it converts an exogenous effort profile $e$ into net feature change $\Delta x = C^\top e$, so the classifier sees score change $(Ch)^\top e$. All of the paper's tractability results hinge on the distribution of $Ch$: in the complete-information case $Ch_0$ is a fixed vector and the ratios $(Ch_0)_f/c_f$ are the 'bang per buck' that determine the optimal profile; under partial uncertainty the assumption that $Ch$ is Gaussian rewrites the probability constraint as $\alpha - \mu_{Ch}^\top e - \Phi^{-1}(\delta)\,\|\Sigma_{Ch}^{1/2} e\|_2 \le 0$, a convex constraint whose KKT analysis yields the closed form $e^\star = \lambda^*(k_1 I + k_2 \Sigma_{Ch})^{-1}\mu_{Ch}$. The same Gaussian object supplies the feasibility boundary in Lemma 5, the diagonal-covariance closed form of Corollary 1, and the experimental behavior of $\beta$-desirability as uncertainty grows.
What would settle it
Run the agent's true optimization on a three-node chain $X_1 \to X_2 \to X_3$ with independent Gaussian edge weights $w_1, w_2$, a known classifier, and $\ell_2$ costs: the contribution of $X_3$ to the score contains the product $w_1 w_2$, so one can compare the true optimal effort (computed by sampling the product distribution) against the claimed formula $\lambda^*(k_1 I + k_2 \Sigma_{Ch})^{-1}\mu_{Ch}$ evaluated with the Gaussian moments; a discrepancy — or, at small $\delta$, non-convexity of the true feasible set — would show the closed form is an approximation, not an exact solution, for general causal graphs.
Extended reading notes
Core claim
The paper's central discovery is that causality turns strategic best-response into linear algebra: because net feature change is $C^\top e$, the effective incentive signal sent by a classifier is the vector $Ch_0$, the total contribution of each feature to the score along all causal paths. With this object the paper proves that under $\ell_1$ costs a rational agent invests in a single feature, the one maximizing $(Ch_0)_f / c_f$, so guaranteeing desirable behavior reduces to making the best bang-per-buck feature desirable; under $\ell_p$ costs with $p>1$ the optimal effort spreads across all contributing features with $e^\star_f \propto ((Ch_0)_f / c_f)^{1/(p-1)}$, and $\beta$-desirability holds when the desirable features' contributions dominate in the corresponding norm, e.g. $\|(Ch_0)_D\|_2 \ge (\beta/\sqrt{1-\beta^2})\|(Ch_0)_U\|_2$ for unit costs at $p=2$. The paper further shows that the set of classifiers inducing desirable effort is generally non-convex when more than one feature is desirable, that it becomes convex when the principal targets a single desirable feature or only bounds undesirable contribution, and that under partial Gaussian uncertainty the agent's chance constraint reduces to a convex inequality and the optimal effort becomes $e^\star = \lambda^*(k_1 I + k_2 \Sigma_{Ch})^{-1}\mu_{Ch}$ — so uncertainty acts like a ridge penalty that diverts effort from high-variance features. Experiments based on a cardiovascular-disease risk graph show agents investing in desirable, unobserved lifestyle features purely through causal propagation, with desirability decreasing in the level of uncertainty.
Load-bearing premise
The tractable incomplete-information results assume that the product $Ch$ of the classifier with the causal contribution matrix is Gaussian, which is guaranteed only when the classifier alone is uncertain or the graph is bipartite; for deeper causal graphs the contribution of a feature is a product of Gaussian edge weights and is not Gaussian, so the closed forms hold as approximations rather than exact characterizations.
Editorial extensions
If this is right
- With $\ell_1$ costs, if a desirable feature offers the unique best contribution-to-cost ratio, no further design effort is needed: every best response is $\beta$-desirable for every $\beta \in (0,1]$.
- With $\ell_p$ costs, $p>1$, the principal can certify desirable behavior in closed form by comparing the $\ell^{2/(p-1)}$-weighted norms of $(Ch_0)$ over desirable versus undesirable features; for unit costs and $p=2$ the condition is the $\ell_2$-norm comparison $\|(Ch_0)_D\|_2 \ge (\beta/\sqrt{1-\beta^2})\|(Ch_0)_U\|_2$.
- Designing classifiers to induce desirable effort is generally non-convex and therefore hard, but convex and efficiently solvable when the principal targets exactly one desirable feature (for $p \in [1,3]$) or relaxes the goal to bounding undesirable contribution.
- Under partial Gaussian uncertainty the agent's best response is a tractable convex program with solution $e^\star_f = \lambda^*(\mu_{Ch})_f / (k_1 + k_2 (\Sigma_{Ch})_f)$ in the diagonal case: effort increases with a feature's expected contribution and decreases with its variance, so variance concentrated on desirable features directly harms $\beta$-desirability.
- In the cardiovascular case study, agents invest substantial effort in desirable lifestyle features even when the classifier puts zero weight on them, because those features causally drive the observed risk factors the classifier does use; raising classifier uncertainty or lowering the required pass probability $\delta$ degrades desirability, and beyond a threshold the agent's problem is infeasible
Reading between the lines
- An implication the authors leave implicit: the closed form $e^\star = \lambda^*(k_1 I + k_2 \Sigma_{Ch})^{-1}\mu_{Ch}$ is structurally a ridge-type shrinkage, which suggests a design lever the paper does not develop — a principal can redirect effort not only by changing classifier weights but by deliberately shaping agents' uncertainty, for instance by publishing a simpler or more stable classifie
- Because $Ch$ is a product of Gaussian edge weights along paths, the closed forms for graph uncertainty are exact only when every path has length one (e.g., bipartite graphs); for deeper DAGs the paper's Gaussian assumption is an approximation, and a natural testable extension is whether that approximation degrades gracefully in the small-variance regime or fails qualitatively in the tails of the p
- A concrete extension with fairness implications: if different population groups hold priors with different variances, the same published classifier will induce group-specific effort profiles, so the $\beta$-desirability gap across groups is, in this model, a function of information asymmetry rather than of the classifier weights alone.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper studies strategic classification in a binary decision problem where a principal deploys a linear classifier and a cost-minimizing agent can exert effort on features embedded in a known DAG. Effort propagates along causal edges through a contribution matrix C, and the agent's objective is to pass the classifier with probability at least 1−δ. The authors introduce a notion of β-desirability to measure whether effort is concentrated on features the principal favors. Under complete information they characterize optimal effort profiles for ℓp costs (single-feature effort for p=1, proportional allocation for p>1), give sufficient conditions for β-desirable best responses, and analyze convexity of the classifier-design space. Under incomplete information, they model Gaussian priors over the classifier and/or edge weights and claim that partial uncertainty leads to a convex program with a closed-form optimal effort profile, while full uncertainty is non-convex. Numerical experiments on a cardiovascular disease dataset illustrate the behavior of β-desirability under classifier uncertainty.
Significance. The complete-information part is clean and potentially useful: the characterization of optimal effort under weighted ℓp costs, the β-desirability conditions, and the convexity results for single-desirable-feature design are coherent and the proofs check out. The paper also makes a good-faith effort to include proofs and a realistic experimental case study. However, the advertised core novelty is the incomplete-information analysis with uncertainty over the causal graph, and that part rests on a false Gaussianity assertion for Model 2. The results survive only when uncertainty is over the classifier (Model 1) or when the graph is bipartite, a much narrower scope than the paper claims. The feasibility characterization (Lemma 5) is also incorrect as stated. These are load-bearing issues, not presentation defects.
major comments (3)
- [§4.1, Eq. (10) and Eq. (11)] The claim that Ch is Gaussian under Model 2 is false for general DAGs. For example, take a chain 1→2→3 with independent Gaussian edge weights w12 and w23 and a deterministic classifier h0 = e3. Then (Ch0)_1 = w12·w23, a product of independent non-degenerate Gaussians, which is not Gaussian. Consequently the chance constraint cannot be rewritten as α − μ_Ch^T e − pδ·||Σ_Ch^{1/2} e||_2 ≤ 0, because (Ch)^T e is not Gaussian. This invalidates the reduction used in Lemma 4 (convexity), Lemma 5 (feasibility), Lemma 6 (ℓ1 multi-feature effort), Theorem 3 (ℓ2 closed form), and Corollary 1 (variance penalization) for Model 2 on general DAGs. Proposition 6 only handles bipartite graphs, and the paper does not scope the Section 4 results to Model 1 or to bipartite graphs. The paper's own discussion in §4.3 notes that non-diagonal Σ_Ch arises for Model 2 on non-bipartite graphs, but that observation is about covariance structure and does not repair the non-Gaussianity.
- [Appendix C.3, Lemma 5] The feasibility condition in Lemma 5 is wrong as stated. Take α > 0 and μ_Ch = 0 with Σ_Ch positive definite. For the regime δ < 1/2 used in Lemma 4, pδ = Φ^{-1}(δ) is negative, so the constraint becomes α − pδ·||Σ_Ch^{1/2} e||_2 ≤ 0, i.e., α + |pδ|·||Σ_Ch^{1/2} e||_2 ≤ 0, which is impossible for every e. Hence the problem is infeasible for all δ < 1/2. The lemma's formula Φ^{-1}(−||Σ_Ch^{-1/2} μ_Ch||_2) evaluates to Φ^{-1}(0) = −∞ in this case, so the lemma incorrectly declares feasibility for every real δ. The proof's derivation around the case d* = Σ_Ch^{-1} μ_Ch also breaks down precisely when μ_Ch = 0, since the Cauchy-Schwarz equality direction is vacuous.
- [Appendix C.2, Proposition 5] The proof of Proposition 5 is not a rigorous mathematical proof. It presents a Monte Carlo plot of f(e) = P[(ωh)e ≥ α] for independent standard normals ω and h and asserts that the function is 'clearly' not concave. An empirical plot does not establish non-convexity of the feasible set or of the optimization problem; it does not rule out, for instance, that the feasible set is convex in some other representation, and it provides no certificate for the claimed counterexample. A rigorous counterexample, or an analytic argument showing a specific non-convex feasible set, is needed to support the negative tractability claim for Model 3.
minor comments (4)
- [§4, first paragraph] The text refers to 'Lemma ??' in the introduction to Section 4; the cross-reference should be to Lemma 4.
- [Theorem 2] The displayed condition in Theorem 2 is typeset in a way that is hard to read: the expression 'βp 1 − β2' does not clearly indicate whether the intended factor is β·p, β_p, or β/√(1−β²). The surrounding discussion and the p=2 reduction should be checked for consistency.
- [Figure 5] Figure 5 has no axis labels and is used as the sole evidence for Proposition 5; beyond the mathematical issue raised above, the figure should at least specify what quantity is plotted and how the Monte Carlo estimate was obtained.
- [§4.3] The discussion of what it means for Σ_Ch to be non-diagonal is helpful, but it should explicitly acknowledge that when G is non-bipartite and uncertainty is over edge weights, the random vector Ch itself is generally not jointly Gaussian, so the tractability claims of §4.1 do not apply in that case.
Circularity Check
No significant circularity: the core derivation chain is self-contained and self-citations are background only.
full rationale
The derivation chain is self-contained. In the complete-information setting, Lemma 1 and Lemma 2 are obtained by solving the agent's explicit convex program (via LP corner-point/duality arguments and KKT conditions), and Theorems 1-2 simply translate those optimal-effort characterizations into β-desirability conditions using Definition 3; no fitted quantity is later relabeled as a prediction. In the incomplete-information setting, the convex reformulation (Lemma 4), feasibility threshold (Lemma 5), ℓ1 structure (Lemma 6), and ℓ2 characterization (Theorem 3) all follow from the paper's stated Gaussian chance-constraint model plus standard convex optimization, and the experiments in Section 5 directly evaluate the derived formulas rather than fitting parameters and re-predicting the fitted values. Self-citations (Bechavod et al. 2021/2022, Cohen et al. 2024, the authors' own prior work) appear only in related-work discussion and are not used as the load-bearing justification of any theorem, so they raise no circularity concern. Two genuine weaknesses exist but they are not circularity: (i) Section 4.1's assertion that 'Ch is a Gaussian random variable' under Model 2 is false for general DAGs containing paths of length at least two, since C is then a product of Gaussian edge weights; this undermines the support of Lemmas 4-6 and Theorem 3 in that regime but is a mathematical-correctness gap rather than a reduction of a result to its own input. (ii) In Appendix C.5, the coefficients in Theorem 3 are defined as k1 = 1/||e*||2 and k2 = -λ*pδ/||Σ^{1/2}e*||2, so the displayed formula is a fixed-point/KKT restatement rather than a fully explicit closed form; again this is an incompleteness in the strength of the claimed characterization, not a circular derivation that assumes the conclusion. No step in the paper equates a prediction with a fitted input, imports a uniqueness theorem from the authors' prior work, or smuggles an ansatz in through citation.
Assumptions & free parameters
assumptions (5)
- domain assumption The causal graph G is a directed acyclic graph; each edge has a linear weight and contribution accumulates along paths as C = Σ_{k=0}^{|F|} A^k.
- domain assumption The agent always knows the topology of the causal graph; incomplete information is only over edge weights and/or classifier parameters, with Gaussian priors.
- ad hoc to paper Under Model 2 (uncertainty over edge weights), the total contribution vector C h is Gaussian.
- domain assumption Agent costs are weighted ℓp-norm costs with cf > 0, as in Eq. (2), and the agent minimizes cost subject to passing with probability at least 1-δ (Eq. (4)).
- standard math For Theorem 3 and Corollary 1, k1 I + k2 Σ_Ch is invertible and Σ_Ch is positive definite where needed; Corollary 1 further assumes Σ_Ch diagonal (Assumption 1).
Cite this review
Pith. "Pith review of Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty." pith.science (2026). https://pith.science/paper/JYSDPRD3
@misc{pith2026250206749,
author = {Pith},
title = {Pith review of: Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty},
year = {2026},
howpublished = {\url{https://pith.science/paper/JYSDPRD3}},
note = {Machine review of arXiv:2502.06749}
}
read the original abstract
We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in a given feature may affect other features. The main goal of our work is to understand \emph{when and how much agent effort is invested towards desirable features}, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them, and the information available to the agent about the classifier and the feature causal graph. In the complete information case, when agents know the classifier and the causal structure of the problem, we derive conditions ensuring that rational agents focus on features favored by the principal. We show that designing classifiers to induce desirable behavior is generally non-convex, though tractable in special cases. We also extend our analysis to settings where agents have incomplete information about the classifier or the causal graph. While optimal effort selection is again a non-convex problem under general uncertainty, we highlight special cases of partial uncertainty where this selection problem becomes tractable. Our results indicate that uncertainty drives agents to favor features with higher expected importance and lower variance, potentially misaligning with principal preferences. Finally, numerical experiments based on a cardiovascular disease risk study illustrate how to incentivize desirable modifications under uncertainty.
Figures
Figures from the paper (2 more)
Forward citations
Cited by 4 Pith papers
-
Linear Strategic Classification with Endogenous Improvements
In a linear strategic-classification model where manipulation can genuinely improve outcomes, the optimal strategic classifier is a parallel shift of the Bayes boundary, and it is a provably better proxy for the impro...
-
A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization
A smoothed matrix-polar spectral gradient flow for Muon-type optimization is globally convergent with O(1/T), O(1/t), and exponential rates, and its local advantage over the Frobenius direction is characterized by the...
-
The Disparate Effects of Partial Information in Bayesian Strategic Learning
For Bayesian strategic agents, score and utility disparities between cost-differentiated groups remain bounded and can be minimized at intermediate transparency, whereas naive agents produce unbounded utility disparit...
-
Desirable Effort Fairness and Optimality Trade-offs in Strategic Learning
Constraining a strategic classifier to keep desirable-effort incentives fair between two groups costs the principal an explicit accuracy or welfare loss bounded by the fairness tolerance beta.
Reference graph
Works this paper leans on
-
[1]
The strategic perceptron
Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita. The strategic perceptron. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 6--25, 2021
2021
-
[2]
On classification of strategic agents who can both game and improve
Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita. On classification of strategic agents who can both game and improve. In 3rd Symposium on Foundations of Responsible Computing, 2022
work page 2022
-
[3]
The economics of moral hazard: further comment
Kenneth J Arrow. The economics of moral hazard: further comment. The American economic review, 58 0 (3): 0 537--539, 1968
work page 1968
-
[4]
Uncertainty and the welfare economics of medical care
Kenneth J Arrow. Uncertainty and the welfare economics of medical care. In Uncertainty in economics, pages 345--375. Elsevier, 1978
work page 1978
-
[5]
Gaming helps! learning from strategic interactions in natural dynamics
Yahav Bechavod, Katrina Ligett, Steven Wu, and Juba Ziani. Gaming helps! learning from strategic interactions in natural dynamics. In International Conference on Artificial Intelligence and Statistics, pages 1234--1242. PMLR, 2021
2021
-
[6]
Information discrepancy in strategic learning
Yahav Bechavod, Chara Podimata, Steven Wu, and Juba Ziani. Information discrepancy in strategic learning. In International Conference on Machine Learning, pages 1691--1715. PMLR, 2022
work page 2022
-
[7]
Introduction to linear optimization
Dimitris Bertsimas and John Tsitsiklis. Introduction to linear optimization. 1997
work page 1997
-
[8]
The role of randomness and noise in strategic classification
Mark Braverman and Sumegha Garg. The role of randomness and noise in strategic classification. In 1st Symposium on Foundations of Responsible Computing, 2020
work page 2020
Show all 36 references
-
[9]
Learning strategy-aware linear classifiers
Yiling Chen, Yang Liu, and Chara Podimata. Learning strategy-aware linear classifiers. Advances in Neural Information Processing Systems, 33: 0 15265--15276, 2020
2020
-
[10]
Bayesian strategic classification, 2024
Lee Cohen, Saeed Sharifi-Malvajerdi, Kevin Stangl, Ali Vakilian, and Juba Ziani. Bayesian strategic classification, 2024. URL https://arxiv.org/abs/2402.08758
2024 arXiv
-
[11]
Strategic classification from revealed preferences
Jinshuo Dong, Aaron Roth, Zachary Schutzman, Bo Waggoner, and Zhiwei Steven Wu. Strategic classification from revealed preferences. In Proceedings of the 2018 ACM Conference on Economics and Computation, pages 55--70, 2018
2018
-
[12]
The double-edged sword of behavioral responses in strategic classification: Theory and user studies
Raman Ebrahimi, Kristen Vaccaro, and Parinaz Naghizadeh. The double-edged sword of behavioral responses in strategic classification: Theory and user studies. arXiv preprint arXiv:2410.18066, 2024
2024 arXiv
-
[13]
Price of privacy in the keynesian beauty contest
Hadi Elzayn and Zachary Schutzman. Price of privacy in the keynesian beauty contest. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 845--863, 2019
2019
-
[14]
Group-fair classification with strategic agents
Andrew Estornell, Sanmay Das, Yang Liu, and Yevgeniy Vorobeychik. Group-fair classification with strategic agents. In Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency, pages 389--399, 2023
2023
-
[15]
Strategic classification in the dark
Ganesh Ghalme, Vineet Nair, Itay Eilat, Inbal Talgam-Cohen, and Nir Rosenfeld. Strategic classification in the dark. In International Conference on Machine Learning, pages 3672--3681. PMLR, 2021
2021
-
[16]
An analysis of the principal-agent problem
Sanford J Grossman and Oliver D Hart. An analysis of the principal-agent problem. In Foundations of Insurance Economics: Readings in Economics and Finance, pages 302--340. Springer, 1992
1992
-
[17]
Strategic classification
Moritz Hardt, Nimrod Megiddo, Christos Papadimitriou, and Mary Wootters. Strategic classification. In Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, pages 111--122, 2016
2016
-
[18]
Stateful strategic regression
Keegan Harris, Hoda Heidari, and Steven Z Wu. Stateful strategic regression. Advances in Neural Information Processing Systems, 34: 0 28728--28741, 2021
2021
-
[19]
Constructing causal pathways for premature cardiovascular disease mortality using directed acyclic graphs with integrating evidence synthesis and expert knowledge
Wan Shakira Rodzlan Hasani, Kamarul Imran Musa, Xin Wee Chen, and Kueh Yee Cheng. Constructing causal pathways for premature cardiovascular disease mortality using directed acyclic graphs with integrating evidence synthesis and expert knowledge. Scientific Reports, 14 0 (1): 0...
2024
-
[20]
Causal strategic classification: A tale of two shifts
Guy Horowitz and Nir Rosenfeld. Causal strategic classification: A tale of two shifts. In International Conference on Machine Learning, pages 13233--13253. PMLR, 2023
2023
-
[21]
The disparate effects of strategic manipulation
Lily Hu, Nicole Immorlica, and Jennifer Wortman Vaughan. The disparate effects of strategic manipulation. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 259--268, 2019
2019
-
[22]
Causal machine learning: A survey and open problems
Jean Kaddour, Aengus Lynch, Qi Liu, Matt J Kusner, and Ricardo Silva. Causal machine learning: A survey and open problems. arXiv preprint arXiv:2206.15475, 2022
2022 arXiv
-
[23]
How do classifiers induce agents to invest effort strategically? ACM Transactions on Economics and Computation (TEAC), 8 0 (4): 0 1--23, 2020
Jon Kleinberg and Manish Raghavan. How do classifiers induce agents to invest effort strategically? ACM Transactions on Economics and Computation (TEAC), 8 0 (4): 0 1--23, 2020
2020
-
[24]
Information elicitation mechanisms for statistical estimation
Yuqing Kong, Grant Schoenebeck, Biaoshuai Tao, and Fang-Yi Yu. Information elicitation mechanisms for statistical estimation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 2095--2102, 2020
2020
-
[25]
The theory of incentives: the principal-agent model
Jean-Jacques Laffont and David Martimort. The theory of incentives: the principal-agent model. In The theory of incentives. Princeton university press, 2009
2009
-
[26]
Strategic classification with unknown user manipulations
Tosca Lechner, Ruth Urner, and Shai Ben-David. Strategic classification with unknown user manipulations. In International Conference on Machine Learning, pages 18714--18732. PMLR, 2023
2023
-
[27]
The delphi method
Harold A Linstone, Murray Turoff, et al. The delphi method. Addison-Wesley Reading, MA, 1975
1975
-
[28]
Strategic classification is causal modeling in disguise
John Miller, Smitha Milli, and Moritz Hardt. Strategic classification is causal modeling in disguise. In International Conference on Machine Learning, pages 6917--6926. PMLR, 2020
2020
-
[29]
The social cost of strategic classification
Smitha Milli, John Miller, Anca D Dragan, and Moritz Hardt. The social cost of strategic classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 230--239, 2019
2019
-
[30]
The economics of moral hazard: comment
Mark V Pauly. The economics of moral hazard: comment. The american economic review, pages 531--537, 1968
1968
-
[31]
Causality: Models, Reasoning, and Inference
Judea Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2000
2000
-
[32]
The economic theory of agency: The principal's problem
Stephen A Ross. The economic theory of agency: The principal's problem. The American economic review, 63 0 (2): 0 134--139, 1973
1973
-
[33]
Incentives in principal-agent relationships
David E M Sappington. Incentives in principal-agent relationships. Journal of economic Perspectives, 5 0 (2): 0 45--66, 1991
1991
-
[34]
Causal strategic linear regression
Yonadav Shavit, Benjamin Edelman, and Brian Axelrod. Causal strategic linear regression. In International Conference on Machine Learning, pages 8676--8686. PMLR, 2020
2020
-
[35]
Pac-learning for strategic classification
Ravi Sundaram, Anil Vullikanti, Haifeng Xu, and Fan Yao. Pac-learning for strategic classification. Journal of Machine Learning Research, 24 0 (192): 0 1--38, 2023
2023
-
[36]
Fairness interventions as (dis) incentives for strategic manipulation
Xueru Zhang, Mohammad Mahdi Khalili, Kun Jin, Parinaz Naghizadeh, and Mingyan Liu. Fairness interventions as (dis) incentives for strategic manipulation. In International Conference on Machine Learning, pages 26239--26264. PMLR, 2022
2022
Reviewed August 8, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.