Optimal Mechanism Design for Single-Minded Agents

Devanur, Nikhil R.; Goldner, Kira; Saxena, Raghuvansh R.; Schvartzman, Ariel; Weinberg, S. Matthew

doi:10.1145/3391403.3399454

Cited by 9 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, our results also contribute to the literature on menu sizes of optimal and approximately optimal mechanisms (e.g., Hart and Nisan, 2017;Babaioff et al, 2017;Gonczarowski, 2018;Saxena et al, 2018;Devanur et al, 2020) and to the literature on the sample complexity of learning up-to-optimal mechanisms (e.g., Cole and Roughgarden, 2014;Morgenstern and Roughgarden, 2015;Devanur et al, 2016;Gonczarowski and Nisan, 2017;Hartline and Taggart, 2019;Gonczarowski and Weinberg, 2018;Guo et al, 2019).…”

Section: Related Worksupporting

confidence: 62%

Revenue Maximization for Buyers with Outside Options

Gonczarowski¹,

Immorlica²,

Li³

et al. 2021

Preprint

View full text Add to dashboard Cite

We study mechanisms for selling a single item when buyers have private values for their outside options, which they forego by participating in the mechanism. This substantially changes the revenue maximization problem. For example, the seller can strictly benefit from selling lotteries already in the single-buyer setting. We bound the menu size and the sample complexity for the optimal single-buyer mechanism. We then show that posting a single price is in fact optimal under the assumption that the item value distribution has decreasing marginal revenue or monotone hazard rate. Moreover, when there are multiple buyers, we show that sequential posted pricing guarantees a large fraction of the optimal revenue when the item value distribution has decreasing marginal revenue.

show abstract

Section: Related Worksupporting

confidence: 62%

Revenue Maximization for Buyers with Outside Options

Gonczarowski¹,

Immorlica²,

Li³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Our approach tackles optimality for an arbitrary finite number of items and varies the ironing procedure. On a technical level, our ironing procedure yields quasiconcave ironed revenue curves, whereas the ironed revenue curves in Haghpanah and Hartline (2020); Fiat et al (2016); Devanur et al (2020) are concave.…”

Section: Related Literaturementioning

confidence: 95%

“…Fiat et al (2016) studies a two-parameter model, and uses an ironing approach that leads from the revenue curves to their concave closure. Devanur et al (2020) generalizes Fiat et al (2016) to more general orders on the second parameter. Our approach tackles optimality for an arbitrary finite number of items and varies the ironing procedure.…”

Section: Related Literaturementioning

confidence: 99%

The Optimality of Upgrade Pricing

Bergemann¹,

Bonatti²,

Haupt³

et al. 2021

Preprint

View full text Add to dashboard Cite

We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing-a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested.We exhibit two distinct sets of sufficient conditions. The first set of conditions is given by a weak version of monotonicity of types and virtual values, while maintaining a regularity assumption, i.e., that the product-by-product revenue curves are singlepeaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)-the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption.Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer's types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.

show abstract

“…The FedEx problem. The FedEx problem was presented in (Fiat et al 2016) and later studied in (Saxena, Schvartzman, and Weinberg 2018;Devanur et al 2020). In the FedEx problem the seller is faced with a buyer which has a varying patience for the duration of the delivery date of a package.…”

Section: Related Workmentioning

confidence: 99%

Learning Revenue Maximization Using Posted Prices for Stochastic Strategic Patient Buyers

Eitan-Hai

Idan

Mansour

2023

AAAI

View full text Add to dashboard Cite

We consider a seller faced with buyers which have the ability to delay their decision, which we call patience. Each buyer's type is composed of value and patience, and it is sampled i.i.d. from a distribution. The seller, using posted prices, would like to maximize her revenue from selling to the buyer. In this paper, we formalize this setting and characterize the resulting Stackelberg equilibrium, where the seller first commits to her strategy, and then the buyers best respond. Following this, we show how to compute both the optimal pure and mixed strategies. We then consider a learning setting, where the seller does not have access to the distribution over buyer's types. Our main results are the following. We derive a sample complexity bound for the learning of an approximate optimal pure strategy, by computing the fat-shattering dimension of this setting. Moreover, we provide a general sample complexity bound for the approximate optimal mixed strategy. We also consider an online setting and derive a vanishing regret bound with respect to both the optimal pure strategy and the optimal mixed strategy.

show abstract

Optimal Mechanism Design for Single-Minded Agents

Cited by 9 publications

References 17 publications

Revenue Maximization for Buyers with Outside Options

Revenue Maximization for Buyers with Outside Options

The Optimality of Upgrade Pricing

Learning Revenue Maximization Using Posted Prices for Stochastic Strategic Patient Buyers

Contact Info

Product

Resources

About