Payment Rules through Discriminant-Based Classifiers
This work addresses computational efficiency in mechanism design for domains with multi-dimensional types, such as combinatorial auctions and assignment problems, offering a novel computational approach.
The paper tackles the problem of designing payment rules in mechanism design by minimizing expected ex post regret instead of imposing incentive compatibility, adapting machine learning techniques like support vector machines. Experimental results show that this approach produces payment rules with low ex post regret and effectively prevents failures of ex post individual rationality.
In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality.