Mechanism Design under Approximate Incentive Compatibility

Abstract

A fundamental assumption in classical mechanism design is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or a lack of information, and may not be able to perfectly optimize their response to a mechanism. This has motivated the introduction of approximate incentive compatibility (IC) as an appealing solution concept for practical mechanism design. While most of the literature has focused on the analysis of particular approximate IC mechanisms, this paper is the first to study the design of optimal mechanisms in the space of approximate IC mechanisms and to explore how much revenue can be garnered by moving from exact to approximate incentive constraints. In particular, we study the problem of a seller facing one buyer with private values and analyze optimal selling mechanisms under ε-incentive compatibility. We establish that an optimal mechanism needs to randomize as soon as ε > 0 and that no mechanism can garner gains higher than order ε 2/3 . This improves upon state-of-the art results which imply maximum gains of ε 1/2 . Furthermore, we construct a mechanism that is guaranteed to achieve order ε 2/3 additional revenues, leading to a tight characterization of the revenue implications of approximate IC constraints. Our study sheds light on a novel class of optimization problems and the challenges that emerge when relaxing IC constraints. In particular, it brings forward the need to optimize not only over allocations and payments but also over best responses, and we develop a new framework to address this challenge.