Collaboration as a Mechanism for More Robust Strategic Classification

Kun Jin, Ziyuan Huang, Mingyan Liu

Abstract: A conventional strategic classification problem takes on a Stackelberg form: a decision maker commits to a decision rule (e.g., in the form of a binary classifier) and agents best respond to the published decision rule by deciding on an effort level so as to maximize their chance of getting a favorable decision less the cost of the effort. This problem becomes significantly more complex when agents are allowed two types of effort: honest (improvement actions) and dishonest (or cheating/gaming). While the former improves an agent's underlying unobservable states (e.g., certain types of qualification), the latter merely improves an agent's outward observable feature, serving as input to the classifier. Under the natural assumption that honest effort is more costly than cheating, prior work has shown that the decision maker has limited ability to mitigate cheating by simply adjusting the decision rule. In this paper, we consider a collaboration mechanism, which the decision maker establishes at a cost and offers to the agents together with the decision rule. In this case, an agent best responds by choosing not only its effort but also whether to participate in the mechanism and if so, with which other agents it wishes to form a connection or collaboration relation. While agents outside the mechanism remain independent of each other, those inside the mechanism are connected to a group of collaborators and enjoy positive externality in the form of a boost in their observable features and consequently enhanced probability of a favorable decision outcome. We show how the collaboration mechanism can induce agents to participate and take improvement actions over gaming and how it can benefit both parties. We also discuss the social value of the system, including social welfare, social qualification status, and the mechanism surplus.