Bayesian Algorithmic Mechanism Design

TL;DR

This paper explores Bayesian incentive compatibility in algorithmic mechanism design, providing a reduction that transforms approximation algorithms into Bayesian IC mechanisms, addressing the conflict between incentive constraints and computational intractability.

Contribution

It introduces a black-box reduction that converts any approximation algorithm into a Bayesian incentive compatible mechanism with similar approximation guarantees.

Findings

Provides a general method for Bayesian IC mechanism design

Bridges the gap between incentive compatibility and computational efficiency

Enables use of approximation algorithms in incentive-compatible settings

Abstract

The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatible mechanisms, namely that of Vickrey, Clarke, and Groves; and the central approach for circumventing computational obstacles, that of approximation algorithms, are fundamentally incompatible: natural applications of the VCG approach to an approximation algorithm fails to yield an incentive compatible mechanism. We consider relaxing the desideratum of (ex post) incentive compatibility (IC) to Bayesian incentive compatibility (BIC), where truthtelling is a Bayes-Nash equilibrium (the standard notion of incentive compatibility in economics). For welfare maximization in single-parameter agent settings, we give a general black-box reduction that turns any approximation algorithm into a Bayesian incentive compatible mechanism with essentially the same approximation factor.