MICRO/THEORY: Strategic Sampling from Manipulable Data; Professor Xianwen Shi (University of Toronto)

Abstract

We study a game between a decision maker and a data manipulator. The decision maker sequentially samples data to learn a binary state (high or low), while the manipulator can distort the data at a cost. The decision maker chooses when to stop sampling and act, aiming to match the true state, while the manipulator prefers the high action regardless of the state and strategically decides when and how intensely to manipulate. In equilibrium, the decision maker adopts a deterministic stopping rule, while the manipulator initially refrains from manipulation and later randomizes between full manipulation and abstention. Manipulation consistently harms the decision maker's decision quality and payoff, though it does not always benefit the manipulator. Notably, manipulation can reverse the decision maker's preference for sampling methods: while sequential sampling is superior without manipulation, static sampling may outperform it when manipulation is possible. This finding highlights the trade-offs between efficiency and robustness in adversarial learning environments.