Optimal Auctions via the Multiplicative Weight Method

TL;DR

This paper introduces a multiplicative weight update framework for designing optimal Bayesian Incentive Compatible auctions, improving computational efficiency and handling complex constraints and utility functions.

Contribution

It presents a novel, simple method for creating optimal auctions that are computationally efficient and accommodate non-linear utilities and various constraints.

Findings

Framework reduces problem complexity to pseudo-polynomial time.

Designs auctions with ex-post Individual Rationality under constraints.

Handles non-linear utility functions like risk aversion and quitting rights.

Abstract

We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to pseudo-polynomial in parameters that depend on single agent instead of depending on the size of the joint type space. We use this framework to design computationally efficient optimal auctions that satisfy ex-post Individual Rationality in the presence of constraints such as (hard, private) budgets and envy-freeness. We also design optimal auctions when buyers and a seller's utility functions are non-linear. Scenarios with such functions include (a) auctions with "quitting rights", (b) cost to borrow money beyond budget, (c) a seller's and buyers' risk aversion. Finally, we show how our framework also yields optimal auctions for variety of auction settings considered in Cai et al, Alaei et al, albeit with pseudo-polynomial running times.