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Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets

Seamus Somerstep, Yuekai Sun, Ya'acov Ritov

TL;DR

This work extends strategic classification by modeling reverse causal strategic learning, where agents can alter outcomes that propagate to observable features via a known causal mechanism. Through theory and continuous-skill experiments rooted in the Coate–Loury labor-market model, it shows that performatively optimal hiring policies can raise employer rewards and improve labor-force skill and equity in some regimes, while potentially reducing aggregate worker welfare and failing to eradicate discrimination in richer equilibria. The paper analyzes threshold hiring policies, derives welfare comparisons under high- and low-wage conditions, and demonstrates how equity can be improved or degraded depending on market assumptions. Collectively, the results illuminate when anticipation of strategic responses aligns incentives across agents and firms, guiding policy design in two-sided markets with feedback effects.

Abstract

Motivated by equilibrium models of labor markets, we develop a formulation of causal strategic classification in which strategic agents can directly manipulate their outcomes. As an application, we compare employers that anticipate the strategic response of a labor force with employers that do not. We show through a combination of theory and experiment that employers with performatively optimal hiring policies improve employer reward, labor force skill level, and in some cases labor force equity. On the other hand, we demonstrate that performative employers harm labor force utility and fail to prevent discrimination in other cases.

Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets

TL;DR

This work extends strategic classification by modeling reverse causal strategic learning, where agents can alter outcomes that propagate to observable features via a known causal mechanism. Through theory and continuous-skill experiments rooted in the Coate–Loury labor-market model, it shows that performatively optimal hiring policies can raise employer rewards and improve labor-force skill and equity in some regimes, while potentially reducing aggregate worker welfare and failing to eradicate discrimination in richer equilibria. The paper analyzes threshold hiring policies, derives welfare comparisons under high- and low-wage conditions, and demonstrates how equity can be improved or degraded depending on market assumptions. Collectively, the results illuminate when anticipation of strategic responses aligns incentives across agents and firms, guiding policy design in two-sided markets with feedback effects.

Abstract

Motivated by equilibrium models of labor markets, we develop a formulation of causal strategic classification in which strategic agents can directly manipulate their outcomes. As an application, we compare employers that anticipate the strategic response of a labor force with employers that do not. We show through a combination of theory and experiment that employers with performatively optimal hiring policies improve employer reward, labor force skill level, and in some cases labor force equity. On the other hand, we demonstrate that performative employers harm labor force utility and fail to prevent discrimination in other cases.
Paper Structure (26 sections, 6 theorems, 81 equations, 5 figures, 1 algorithm)

This paper contains 26 sections, 6 theorems, 81 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Reverse causal strategic learning
  3. The reverse causal strategic learning problem
  4. Strategic hiring in the Coate-Loury model
  5. Performative Prediction in the Coate-Loury model
  6. Effects of strategic hiring on employer and labor force welfare
  7. Effects of strategic hiring on labor force equity
  8. Experiments on markets with continuous skill levels
  9. Experiments With Linear Utility and Flat Wages
  10. Experiments with non-linear utility and non-flat wages
  11. Conclusion
  12. Stochastic optimization for reverse-causal strategic learning
  13. Learning Set Up
  14. Methodology
  15. Proof of Lemma A.1
  16. ...and 11 more sections

Key Result

Theorem 3.1

If $w > M_G/\delta_1$ and $p_+ > p_-/(\delta_1 \delta_2)$ then the following holds for all stable parameters $\theta_{\text{stab}}$ and all optimal parameters $\theta_{\text{opt}}$:

Figures (5)

  • Figure 1: Worker Welfare and Proportion of Qualified Workers for Optimal and Stable Policies
  • Figure 2: Left: RSGD and Alg 1 ($a=2, w=1, c=5$) // Right: employer Utility Under Policies (Left: $w=1,c=5$ // Right: $w=1, a=2$)
  • Figure 3: Worker Welfare and Proportion of Qualified Workers for Optimal and Stable Policies
  • Figure 4: A market with fair optimal pairs and discriminatory stable pairs
  • Figure 5: Algorithm 1 and RSGD with $a = 4, \: w = 1, \: c = 4$

Theorems & Definitions (20)

  • Example 1.1: hardt2015Strategic
  • Example 2.1: coate1993Will
  • Example 2.2: hron2023modeling, Jagadeesan2023modeling
  • Example 2.3: Example \ref{['ex:coate-loury']} cont
  • Example 2.4: Example \ref{['ex:exposure-games']} cont
  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Lemma A.1
  • ...and 10 more