Payment Rules through Discriminant-Based Classifiers

TL;DR

This paper introduces a machine learning-based method for designing payment rules in mechanism design by minimizing ex post regret, applicable to complex domains with efficiency concerns.

Contribution

It proposes a novel approach using discriminant-based classifiers, specifically support vector machines, to derive incentive-compatible payment rules without traditional constraints.

Findings

Payment rules with low ex post regret are effectively constructed.

Penalizing classification errors helps prevent violations of individual rationality.

Method is applicable to multi-dimensional types and complex outcome rules.

Abstract

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.