Learning under Imitative Strategic Behavior with Unforeseeable Outcomes

TL;DR

This paper models strategic behavior with unforeseeable outcomes using a Stackelberg game, revealing how decision-makers can influence individuals' manipulation and improvement to promote fairness and responsibility.

Contribution

It introduces a novel game-theoretic framework for imitative strategic manipulation with unpredictable outcomes, providing theoretical insights into decision-maker preferences and social implications.

Findings

Decomposition of the objective difference into three interpretable terms.

Decision-maker preferences influence incentives for manipulation and improvement.

Guidelines for socially responsible decision-making based on theoretical analysis.

Abstract

Machine learning systems have been widely used to make decisions about individuals who may behave strategically to receive favorable outcomes, e.g., they may genuinely improve the true labels or manipulate observable features directly to game the system without changing labels. Although both behaviors have been studied (often as two separate problems) in the literature, most works assume individuals can (i) perfectly foresee the outcomes of their behaviors when they best respond; (ii) change their features arbitrarily as long as it is affordable, and the costs they need to pay are deterministic functions of feature changes. In this paper, we consider a different setting and focus on imitative strategic behaviors with unforeseeable outcomes, i.e., individuals manipulate/improve by imitating the features of those with positive labels, but the induced feature changes are unforeseeable. We first propose a Stackelberg game to model the interplay between individuals and the decision-maker, under which we examine how the decision-maker's ability to anticipate individual behavior affects its objective function and the individual's best response. We show that the objective difference between the two can be decomposed into three interpretable terms, with each representing the decision-maker's preference for a certain behavior. By exploring the roles of each term, we theoretically illustrate how a decision-maker with adjusted preferences may simultaneously disincentivize manipulation, incentivize improvement, and promote fairness. Such theoretical results provide a guideline for decision-makers to inform better and socially responsible decisions in practice.