Algorithmic Recourse Under Competition

2026-09-30

AI Summary

This study addresses the failure of algorithmic recourse caused by the dynamic drift of decision thresholds under resource competition. Moving beyond the conventional assumption of fixed thresholds, this work proposes an algorithmic recourse framework for competitive environments that, for the first time, models the dynamic impact of individual competition on acceptance thresholds. Based on the implicit function theorem, an optimization algorithm is developed to jointly optimize recommended actions and target scores, thereby balancing implementation cost against effectiveness. Experimental results demonstrate that personalized targets enhance effectiveness but incur higher costs, whereas universal targets achieve a superior cost-effectiveness ratio within low-to-moderate effectiveness ranges.

Abstract

Algorithmic recourse provides individuals who have received undesirable outcomes from machine learning models with suggestions for minimum-cost improvements to achieve the desired outcome. A central assumption when computing recourse is that the decision rule remains fixed throughout the recourse implementation phase. We challenge this assumption in settings where individuals compete for limited resources. In such settings, widespread recourse implementation can change the acceptance threshold even when the scoring model that is used to evaluate individuals remains the same. This change in acceptance threshold can, in turn, invalidate the original recourse recommendations (i.e., following the recourse may not lead to the desired outcome). To address this problem, we introduce a framework called recourse under competition that jointly optimizes for recommendation recipients and the recommended score target they need to satisfy to balance the recourse cost and post-shift validity among initially rejected individuals. We develop an algorithm based on the Implicit Function Theorem and empirically analyze its performance. Experiments on synthetic and real datasets show that personalized score targets can achieve higher validity, albeit at a higher cost. In contrast, common score targets generally offer favorable cost-validity trade-offs for lower to medium validity values.

Problem

• Algorithmic Recourse
• Competition
• Threshold Shift
• Validity

Innovation

• Algorithmic Recourse
• Competition
• Implicit Function Theorem
• Score Target Optimization
• Threshold Shift