Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Equal Merit Does Not Imply Equality: Discrimination at Equilibrium in a Hiring Market with Symmetric Agents

Serafina Kamp, Benjamin Fish

TL;DR

The paper analyzes discrimination in hiring markets where agents are resource-symmetric, showing that strategy consensus in Rubinstein-style bargaining can produce asymmetric equilibrium wages even when merit is equal. It provides a two-pronged contribution: first, proving the existence of discriminatory equilibria via credible threats under a symmetric market with endogenous outside options; and second, initiating an online-learning analysis (FTRL with discretization) to show convergence to Nash equilibria, including asymmetric ones, in a simplified bargaining setting. The results highlight non-distributional pathways to inequality and demonstrate how learning dynamics can reinforce or create discriminatory outcomes, suggesting caution for algorithmic interventions that assume distributive equality will automatically resolve disparities. Overall, the work motivates further study of endogenous, non-distributional mechanisms of inequality in ML and economic bargaining contexts, with implications for fairness metrics and policy design.

Abstract

Machine learning has grown in popularity to help assign resources and make decisions about users, which can result in discrimination. This includes hiring markets, where employers have increasingly been interested in using automated tools to help hire candidates. In response, there has been significant effort to understand and mitigate the sources of discrimination in these tools. However, previous work has largely assumed that discrimination, in any area of ML, is the result of some initial \textit{unequal distribution of resources} across groups: One group is on average less qualified, there is less training data for one group, or the classifier is less accurate on one group, etc. However, recent work have suggested that there are other sources of discrimination, such as relational inequality, that are notably non-distributional. First, we show consensus in strategy choice is a non-distributional source of inequality at equilibrium in games: We provide subgame perfect equilibria in a simple sequential model of a hiring market with Rubinstein-style bargaining between firms and candidates that exhibits asymmetric wages resulting from differences in agents' threat strategies during bargaining. Second, we give an initial analysis of how agents could learn such strategies via convergence of an online learning algorithm to asymmetric equilibria. Ultimately, this work motivates the further study of endogenous, possibly non-distributional, mechanisms of inequality in ML.

Equal Merit Does Not Imply Equality: Discrimination at Equilibrium in a Hiring Market with Symmetric Agents

TL;DR

The paper analyzes discrimination in hiring markets where agents are resource-symmetric, showing that strategy consensus in Rubinstein-style bargaining can produce asymmetric equilibrium wages even when merit is equal. It provides a two-pronged contribution: first, proving the existence of discriminatory equilibria via credible threats under a symmetric market with endogenous outside options; and second, initiating an online-learning analysis (FTRL with discretization) to show convergence to Nash equilibria, including asymmetric ones, in a simplified bargaining setting. The results highlight non-distributional pathways to inequality and demonstrate how learning dynamics can reinforce or create discriminatory outcomes, suggesting caution for algorithmic interventions that assume distributive equality will automatically resolve disparities. Overall, the work motivates further study of endogenous, non-distributional mechanisms of inequality in ML and economic bargaining contexts, with implications for fairness metrics and policy design.

Abstract

Machine learning has grown in popularity to help assign resources and make decisions about users, which can result in discrimination. This includes hiring markets, where employers have increasingly been interested in using automated tools to help hire candidates. In response, there has been significant effort to understand and mitigate the sources of discrimination in these tools. However, previous work has largely assumed that discrimination, in any area of ML, is the result of some initial \textit{unequal distribution of resources} across groups: One group is on average less qualified, there is less training data for one group, or the classifier is less accurate on one group, etc. However, recent work have suggested that there are other sources of discrimination, such as relational inequality, that are notably non-distributional. First, we show consensus in strategy choice is a non-distributional source of inequality at equilibrium in games: We provide subgame perfect equilibria in a simple sequential model of a hiring market with Rubinstein-style bargaining between firms and candidates that exhibits asymmetric wages resulting from differences in agents' threat strategies during bargaining. Second, we give an initial analysis of how agents could learn such strategies via convergence of an online learning algorithm to asymmetric equilibria. Ultimately, this work motivates the further study of endogenous, possibly non-distributional, mechanisms of inequality in ML.

Paper Structure

This paper contains 22 sections, 20 theorems, 117 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Discrimination Against Agents of Equal Merit
  4. Discrimination Analysis in Markets
  5. Critiques of Distributional Equality
  6. Piecewise Linear Optimization
  7. Discriminatory Equilibria via Threats
  8. The Market Model
  9. Disparity at Equilibrium
  10. Discussion
  11. Discriminatory Equilibria via Learning
  12. Simplified Bargaining Game
  13. Learning to Bargain via FTRL
  14. Convergence to Nash Equilibrium
  15. Disparity at Equilibrium
  16. ...and 7 more sections

Key Result

Theorem 1

If $\tau \le \frac{\delta^2}{1+\delta}$, then for any $p\in[0,1]$ and any $w_1,w_2\in[0,1]$ that satisfy there exists an SPE where the firms obtain an expected payoff of $pw_1+(1-p)w_2$, the $c_1$ candidates get an expected payoff of $1-w_1$ and the $c_2$ candidates get an expected payoff of $1-w_2$ at equilibrium.

Figures (3)

  • Figure 1: The progression of the market over time is shown on the right with one round of the bargaining phase expanded on the left.
  • Figure 2: Simulation results for NE outcomes of agents learning strategies in $\mathcal{G}^{(2)}$. The setting is $T=300, M=40, D=16, p=1, \alpha_P = (0.125, 0.375), \alpha_R = (0.375, 0.875)$. The initial strategy of the proposer varies from $\{\frac{1}{D},\frac{3}{D}\ldots, \frac{D-1}{D}\}$ in both strategy dimensions. The color of each cell represents the average payoff to the proposer playing that initial strategy over the initial strategies the responder plays from the same set.
  • Figure :

Theorems & Definitions (39)

  • Theorem 1
  • Proposition 3
  • Theorem 4
  • Theorem 5
  • Example 6
  • Theorem 1
  • Proposition 2
  • proof : Proof outline
  • proof
  • Proposition 1
  • ...and 29 more