Trust in Persuasion for Binary Adversarial Classification

A sender has access to a dataset which is split into two classes. The sender observes these data points which get generated uniformly at random and sends the receiver a message about its observation. The receiver's goal is to correctly classify the data point from the message sent by the sender. The sender wants to persuade the receiver to choose a class that maximizes the sender's utility which is dependent on how a data point is classified. We study this interaction as a Stackelberg game. We show that if the sender wants to get some proportion of data points of a particular label misclassified using a message, then at every Stackelberg equilibrium strategy, it should use the same message for equal or more proportion of data points whose true label is that particular label. We study two special classes of utility functions and show that the obscureness of the sender, which is the maximum number of data points that can be misclassified at equilibrium, is equal to the total number of data points of the least frequent label in the dataset. In addition to quantifying obscureness, we also quantify the minimum information that needs to be revealed by the sender at Stackelberg equilibrium, which we call the informativeness of the sender. We prove these results by characterizing the Stackelberg equilibrium game and the informativeness of the sender via two linear programs we introduced in this paper. The linear program characterization is the key contribution of our paper.