Revenue Maximization for Buyers with Costly Participation

Yannai A. Gonczarowski, Nicole Immorlica, Yingkai Li and Brendan Lucier

Papers from arXiv.org

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.

Date: 2021-03, Revised 2023-11
New Economics Papers: this item is included in nep-com, nep-des and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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