The Randomized Communication Complexity of Randomized Auctions

TL;DR

This paper investigates the communication complexity of randomized auctions, demonstrating that randomized protocols can be exponentially more efficient than deterministic ones in incentivizing revenue-optimal auctions, and provides lower bounds for approximate revenue maximization.

Contribution

It introduces simple, incentive compatible, revenue-optimal auction protocols with significantly reduced expected communication complexity and establishes the first exponential separation between incentivizing and implementing Bayesian incentive compatible rules.

Findings

Randomized auction protocols are much more communication-efficient than deterministic ones.

The paper provides nearly matching lower bounds for approximately-revenue-optimal auctions.

It proves the first exponential separation between incentivizing and implementing Bayesian incentive compatible rules.

Abstract

We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over $n$ items. Motivated by the fact that revenue-optimal auctions are randomized [Tha04,MV10,BCKW10,Pav11,HR15] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [BGN17]),we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [FS09].