Revenue Maximization for Buyers with Costly Participation

TL;DR

This paper develops mechanisms for selling to buyers with private participation costs, achieving near-optimal revenue with polynomial algorithms, and identifies conditions where simple posted pricing is optimal or nearly so.

Contribution

It introduces a polynomial-time approximation scheme for multi-buyer revenue maximization with participation costs and characterizes when simple posted prices are optimal.

Findings

Constructed a $(2+ ext{epsilon})$-approximate mechanism for multiple buyers.

Provided an FPTAS for the single-buyer case.

Identified conditions where posted pricing is optimal or near-optimal.

Abstract

We study mechanisms for selling a single item when buyers have private costs for participating in the mechanism. An agent's participation cost can also be interpreted as an outside option value that she must forego to participate. This substantially changes the revenue maximization problem, which becomes non-convex in the presence of participation costs. For multiple buyers, we show how to construct a $(2+\epsilon)$-approximately revenue-optimal mechanism in polynomial time. Our approach makes use of a many-buyers-to-single-buyer reduction, and in the single-buyer case our mechanism improves to an FPTAS. We also bound the menu size and the sample complexity for the optimal single-buyer mechanism. Moreover, we show that posting a single price in the single-buyer case is in fact optimal under the assumption that either (1) the participation cost is independent of the value, and the value distribution has decreasing marginal revenue or monotone hazard rate; or (2) the participation cost is a concave function of the value. When there are multiple buyers, we show that sequential posted pricing guarantees a large fraction of the optimal revenue under similar conditions.