Strategic Multi-class Classification for Non-uniform Preferences and its Relation to Incentive Compatibility

Motivated by the problem of university admissions, we study the problem of correctly classifying the label of a feature vector when a sender can manipulate this vector to get a desired label. There are two players: sender and receiver and both know the target function over the feature vectors. The sender privately observes a feature vector and manipulates it according to its payoff criteria and sends it to the receiver. The receiver would like to perform multi-class classification to maximize the number of points for which it can recover the original label of the feature vector known to the sender. We pose this problem as a Stackelberg game with the receiver as the leader. Through this we characterise the optimal classifier in terms of the independence number of a certain graph which depends on the utility and cost of the sender and the target function. As a corollary, we characterise the optimal strategy of the receiver for the problem of strategic communication with cost. Finally we show that if the target function is incentive compatible condition, then the receiver can correctly classify all feature vectors.