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Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification

Sura Alhanouti, Parinaz Naghizadeh

TL;DR

This paper analyzes how individuals strategically respond to algorithmic decisions by choosing between manipulating observable features or genuinely improving qualifications, modeled as a Stackelberg game where the firm first selects a threshold-based classifier. It introduces a stochastic, action-specific boost model for manipulation and improvement, with distinct costs and stochastic efficacies, and examines fairness constraints (Equality of Opportunity and Demographic Parity) under strategic responses. Key findings show that anticipating strategic behavior can not only curb manipulation but also incentivize improvement, particularly for unqualified agents, while still permitting beneficial manipulation by some qualified individuals; fairness interventions can have nuanced effects, potentially reducing improvement incentives for disadvantaged groups when the firm fails to account for strategic responses, whereas a strategic firm can meet fairness goals with smaller utility losses by leveraging thresholds and response dynamics. Theoretical characterization of agent best-responses, post-strategic population statistics, and optimal classifier thresholds is complemented by extensive numerical experiments across single- and two-group settings, highlighting the practical implications for deploying fair and robust decision rules in the presence of strategic users.

Abstract

As machine learning algorithms increasingly influence critical decision making in different application areas, understanding human strategic behavior in response to these systems becomes vital. We explore individuals' choice between genuinely improving their qualifications (``improvement'') vs. attempting to deceive the algorithm by manipulating their features (``manipulation'') in response to an algorithmic decision system. We further investigate an algorithm designer's ability to shape these strategic responses, and its fairness implications. Specifically, we formulate these interactions as a Stackelberg game, where a firm deploys a (fair) classifier, and individuals strategically respond. Our model incorporates both different costs and stochastic efficacy for manipulation and improvement. The analysis reveals different potential classes of agent responses, and characterizes optimal classifiers accordingly. Based on these, we highlight the impact of the firm's anticipation of strategic behavior, identifying when and why a (fair) strategic policy can not only prevent manipulation, but also incentivize agents to opt for improvement.

Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification

TL;DR

This paper analyzes how individuals strategically respond to algorithmic decisions by choosing between manipulating observable features or genuinely improving qualifications, modeled as a Stackelberg game where the firm first selects a threshold-based classifier. It introduces a stochastic, action-specific boost model for manipulation and improvement, with distinct costs and stochastic efficacies, and examines fairness constraints (Equality of Opportunity and Demographic Parity) under strategic responses. Key findings show that anticipating strategic behavior can not only curb manipulation but also incentivize improvement, particularly for unqualified agents, while still permitting beneficial manipulation by some qualified individuals; fairness interventions can have nuanced effects, potentially reducing improvement incentives for disadvantaged groups when the firm fails to account for strategic responses, whereas a strategic firm can meet fairness goals with smaller utility losses by leveraging thresholds and response dynamics. Theoretical characterization of agent best-responses, post-strategic population statistics, and optimal classifier thresholds is complemented by extensive numerical experiments across single- and two-group settings, highlighting the practical implications for deploying fair and robust decision rules in the presence of strategic users.

Abstract

As machine learning algorithms increasingly influence critical decision making in different application areas, understanding human strategic behavior in response to these systems becomes vital. We explore individuals' choice between genuinely improving their qualifications (``improvement'') vs. attempting to deceive the algorithm by manipulating their features (``manipulation'') in response to an algorithmic decision system. We further investigate an algorithm designer's ability to shape these strategic responses, and its fairness implications. Specifically, we formulate these interactions as a Stackelberg game, where a firm deploys a (fair) classifier, and individuals strategically respond. Our model incorporates both different costs and stochastic efficacy for manipulation and improvement. The analysis reveals different potential classes of agent responses, and characterizes optimal classifiers accordingly. Based on these, we highlight the impact of the firm's anticipation of strategic behavior, identifying when and why a (fair) strategic policy can not only prevent manipulation, but also incentivize agents to opt for improvement.
Paper Structure (34 sections, 9 theorems, 30 equations, 12 figures, 3 tables)

This paper contains 34 sections, 9 theorems, 30 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setting and Preliminaries
  4. Agents' Strategic Behavior
  5. Illustration: uniform boost distributions
  6. Post-strategic population statistics
  7. The Firm's Optimal Policy
  8. Effects of Anticipating Strategic Behavior
  9. Intuitive interpretation and key takeaways of Proposition \ref{['prop:firm_impact_comp']}
  10. The costly improvement (Type 3) equilibrium.
  11. The affordable improvement (Type 1) equilibrium.
  12. Effects of fairness interventions
  13. Numerical Experiments
  14. Single-group experiment setup.
  15. Strategic vs. non-strategic (unfair) firms.
  16. ...and 19 more sections

Key Result

Proposition 2

If $\mathbf{f}^y_{s}$ is unique, the agents' optimal response $w^*_{s}(x,y)=\arg\max_{w\in\{M,I,N\}} u_s(x,y,w)$ to a given threshold $\theta_s$ will be one of the three types outlined in Table table:prop-agent-br-generic.

Figures (12)

  • Figure 1: Agent best-responses identified in Proposition \ref{['prop:agents-br-generic']}.
  • Figure 2: The effect of the non-strategic and strategic policies on agents' strategic behavior in different equilibrium types. The curves represent the label $Y$ agents' feature distributions.
  • Figure 3: Unfair optimal non-strategic vs. strategic policies' comparison when varying pre-strategic $\alpha_s$.
  • Figure 4: Unfair non-strategic vs. strategic policies' impact on post-strategic $\hat{\alpha}_s$ across pre-strategic $\alpha_s$.
  • Figure 5: Firm's utility and optimal thresholds when imposing fairness constraints.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Definition 1
  • Proposition 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • Proposition 8
  • Corollary 9
  • Lemma 10
  • ...and 1 more