Send Mixed Signals -- Earn More, Work Less

TL;DR

This paper demonstrates that in probabilistic second-price auctions, finding optimal mixed signaling schemes is computationally feasible and can significantly outperform pure schemes, with practical implications for auction revenue maximization.

Contribution

It proves polynomial-time solvability of optimal mixed signaling schemes and establishes their potential to double revenue compared to pure schemes.

Findings

Optimal mixed signaling schemes can be computed in polynomial time.

Mixed schemes can generate twice the revenue of pure schemes.

A lower bound on revenue from mixed signaling schemes is established.

Abstract

Emek et al. presented a model of probabilistic single-item second price auctions where an auctioneer who is informed about the type of an item for sale, broadcasts a signal about this type to uninformed bidders. They proved that finding the optimal (for the purpose of generating revenue) {\em pure} signaling scheme is strongly NP-hard. In contrast, we prove that finding the optimal {\em mixed} signaling scheme can be done in polynomial time using linear programming. For the proof, we show that the problem is strongly related to a problem of optimally bundling divisible goods for auctioning. We also prove that a mixed signaling scheme can in some cases generate twice as much revenue as the best pure signaling scheme and we prove a generally applicable lower bound on the revenue generated by the best mixed signaling scheme.