Strategic Classification With Externalities

TL;DR

This paper introduces a new strategic classification model accounting for externalities among agents, providing theoretical foundations for learning classifiers robust to multiple interacting strategic agents.

Contribution

It models inter-agent externalities in strategic classification as a Stackelberg and simultaneous game, proving the uniqueness and computability of equilibrium, and establishing PAC learning guarantees.

Findings

Unique pure Nash Equilibrium can be efficiently computed.

Classifiers can be learned to minimize loss despite strategic manipulation.

Theoretical framework for classifiers robust to multiple strategic agents.

Abstract

We propose a new variant of the strategic classification problem: a principal reveals a classifier, and $n$ agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially allows the manipulation of one agent to affect another; that is, it explicitly captures inter-agent externalities. The principal-agent interactions are formally modeled as a Stackelberg game, with the resulting agent manipulation dynamics captured as a simultaneous game. We show that under certain assumptions, the pure Nash Equilibrium of this agent manipulation game is unique and can be efficiently computed. Leveraging this result, PAC learning guarantees are established for the learner: informally, we show that it is possible to learn classifiers that minimize loss on the distribution, even when a random number of agents are manipulating their way to a pure Nash Equilibrium. We also comment on the optimization of such classifiers through gradient-based approaches. This work sets the theoretical foundations for a more realistic analysis of classifiers that are robust against multiple strategic actors interacting in a common environment.