Payment Rules through Discriminant-Based Classifiers

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.



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1 Introduction

Mechanism design studies situations where a set of agents each hold private information about their preferences over different outcomes. The designer chooses a center that receives claims about such preferences, selects and enforces an outcome, and optionally collects payments. The classical approach is to impose incentive compatibility, ensuring that agents truthfully report their preferences in strategic equilibrium. Subject to this constraint, the goal is to identify a mechanism, i.e., a way of choosing an outcome and payments based on agents’ reports, that optimizes a given design objective like social welfare, revenue, or some notion of fairness.

There are, however, significant challenges associated with this classical approach. First of all, it can be analytically cumbersome to derive optimal mechanisms for domains that are “multi-dimensional” in the sense that each agent’s private information is described through more than a single number, and few results are known in this case.111One example of a multi-dimensional domain is a combinatorial auction, where an agent’s preferences are described by a numerical value for each of several different bundles of items. Second, incentive compatibility can be costly, in that adopting it as a hard constraint can preclude mechanisms with useful economic properties. For example, imposing the strongest form of incentive compatibility, truthfulness in a dominant strategy equilibrium or strategyproofness, necessarily leads to poor revenue, vulnerability to collusion, and vulnerability to false-name bidding in combinatorial auctions where valuations exhibit complementarities among items (missing[missing], missing)