How do agents invest strategically under persistent improvement?

Tian Xie, Xuwei Tan, Xueru Zhang

Keywords: Strategic Classification, Stackelberg Game, Population Dynamics

TL;DR: This paper studies the strategic interactions between agents and a decision-maker when agent action has delayed and persistent effects with diminishing utility.

Abstract: This paper studies algorithmic decision-making under human's strategic behavior, where a decision-maker uses an algorithm to make decisions about human agents, and the latter with information about the algorithm may exert effort strategically and improve to receive favorable decisions. Unlike prior works that assume agents benefit from their efforts immediately, we consider realistic scenarios where the impacts of these efforts are persistent and agents benefit from efforts by making improvements gradually. However, the agent's utility also diminishes as time goes on. We first develop a dynamic model to characterize persistent improvements and based on this construct a Stackelberg game to model the interplay between agents and the decision-maker. We analytically characterize the equilibrium strategies and identify conditions under which agents have incentives to improve. With the dynamics, we then study how the decision-maker can design an optimal policy to incentivize the largest improvements inside the agent population. We also extend the model to settings where (1) agents may be dishonest and game the algorithm into making favorable but erroneous decisions; (2) honest efforts are forgettable and not sufficient to guarantee persistent improvements. With the extended models, we further examine conditions under which agents prefer honest efforts over dishonest behavior and the impacts of forgettable efforts.

Primary Area: societal considerations including fairness, safety, privacy

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Submission Number: 1108