Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility

TL;DR

This paper extends the understanding of simple pricing mechanisms, showing that anonymous pricing approximates optimal revenue for various non-linear utility models under a generalized regularity condition.

Contribution

It introduces a new parameterization of regularity that applies to non-linear utilities and demonstrates that anonymous pricing remains a constant-factor approximation in these settings.

Findings

Anonymous pricing approximates optimal revenue for agents with public and private budgets.

The approximation extends to certain risk-averse utility models.

A new regularity framework applies to non-linear utility agents.

Abstract

The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.