Simple vs Optimal Mechanisms in Auctions with Convex Payments

TL;DR

This paper studies auction mechanisms with convex payment functions, providing approximation guarantees and experimental evidence that multi-bidder allocations outperform traditional single-bidder focus in revenue maximization.

Contribution

It introduces constant factor approximation mechanisms for convex payment auctions, both prior-free and detail free, with theoretical guarantees and experimental validation.

Findings

Mechanisms achieve at least 80% of optimal revenue on average.

Allocating to multiple bidders is more effective than to only the highest-value bidder.

Both theoretical and experimental results support multi-bidder allocations in convex payment settings.

Abstract

We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide constant factor approximation guarantees for mechanisms that are independent of bidders' private information (i.e., prior-free), and for mechanisms that rely to an increasing extent on that information (i.e., detail free). We also describe experiments, which show that for randomly drawn monotone hazard rate distributions, our mechanisms achieve at least 80\% of the optimal revenue, on average. Both our theoretical and experimental results show that in the convex payment setting, it is desirable to allocate across multiple bidders, rather than only to bidders with the highest (virtual) value, as in the traditional quasi-linear utility setting.