Learning User Preferences in Mechanism Design

In designing a mechanism for allocation of a divisible resource, the designer needs to know the player utility functions, which are often infinitely dimensional, in order to choose the appropriate pricing and allocation rules. This paper utilizes Gaussian process regression learning techniques to infer general player preferences by a designer in a mechanism design setting. In pricing mechanisms, the price taking players are charged with the appropriate value of Lagrange multiplier, in order to achieve efficiency. This value is obtained iteratively through learning. Likewise, the reserve price in auction mechanisms with price anticipating players, a parameter in allocation and pricing rules, is modified iteratively using online learning to move the system solution to near efficiency. A numerical example illustrates the approach and demonstrates the online learning algorithm.