The menu-size complexity of revenue approximation

Babaioff, Moshe; Gonczarowski, Yannai A.; Nisan, Noam

doi:10.1016/j.geb.2021.03.001

Cited by 20 publications

(72 citation statements)

References 27 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

Self Cite

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…chooses the IC action that maximizes the principal's expected payoff. 5 We say contract p implements or incentivizes action a i if given p the agent chooses a i (namely a i is IC and survives tie-breaking). If there exists such a contract for action a i we say a i is implementable, and slightly abusing notation we sometimes refer to the implementing contract as an IC contract.…”

Section: Contracts and Incentivesmentioning

confidence: 99%

“…Both reflect the typical situation in which the principal has "deeper pockets" than the agent and is thus the better bearer of expenses/risks. 5 The idea is that one could perturb the payment schedule slightly to make the desired action uniquely optimal for the agent. For further discussion see [13, p. 8].…”

Section: Contracts and Incentivesmentioning

confidence: 99%

The Complexity of Contracts

Dütting¹,

Roughgarden²,

Talgam-Cohen³

2021

SIAM J. Comput.

View full text Add to dashboard Cite

We initiate the study of computing (near-)optimal contracts in succinctly representable principal-agent settings. Here optimality means maximizing the principal's expected payoff over all incentive-compatible contracts-known in economics as "second-best" solutions. We also study a natural relaxation to approximately incentive-compatible contracts.We focus on principal-agent settings with succinctly described (and exponentially large) outcome spaces. We show that the computational complexity of computing a near-optimal contract depends fundamentally on the number of agent actions. For settings with a constant number of actions, we present a fully polynomial-time approximation scheme (FPTAS) for the separation oracle of the dual of the problem of minimizing the principal's payment to the agent, and use this subroutine to efficiently compute a δ-incentive-compatible (δ-IC) contract whose expected payoff matches or surpasses that of the optimal IC contract.With an arbitrary number of actions, we prove that the problem is hard to approximate within any constant c. This inapproximability result holds even for δ-IC contracts where δ is a sufficiently rapidly-decaying function of c. On the positive side, we show that simple linear δ-IC contracts with constant δ are sufficient to achieve a constant-factor approximation of the "first-best" (full-welfareextracting) solution, and that such a contract can be computed in polynomial time.

show abstract

“…This was later extended to multiple buyers [Yao 2015], as well as buyers with more general valuations (e.g., subadditive [Rubinstein and Weinberg 2015], valuations with a common-value component [Bateni et al 2015], and valuations with complements [Eden et al 2017]). Others have studied the tradeoff between the complexity and approximation ratio of an auction, along with the design of smallmenu mechanisms in various settings [Babaioff et al 2017;Cheng et al 2015;Dughmi et al 2014;Hart and Nisan 2013;Tang and Wang 2017].…”

Section: Related Workmentioning

confidence: 99%

A Simple Mechanism for a Budget-Constrained Buyer

Cheng

Gravin

Munagala

et al. 2021

ACM Trans. Econ. Comput.

View full text Add to dashboard Cite

We study a classic Bayesian mechanism design setting of monopoly problem for an additive buyer in the presence of budgets. In this setting, a monopolist seller with m heterogeneous items faces a single buyer and seeks to maximize her revenue. The buyer has a budget and additive valuations drawn independently for each item from (non-identical) distributions. We show that when the buyer’s budget is publicly known, it is better to sell each item separately; selling the grand bundle extracts a constant fraction of the optimal revenue. When the budget is private, we consider a standard Bayesian setting where buyer’s budget b is drawn from a known distribution B . We show that if b is independent of the valuations (which is necessary) and distribution B satisfies monotone hazard rate condition, then selling items separately or in a grand bundle is still approximately optimal.

show abstract

The menu-size complexity of revenue approximation

Cited by 20 publications

References 27 publications

Revenue Maximization for Buyers with Outside Options

Revenue Maximization for Buyers with Outside Options

The Complexity of Contracts

A Simple Mechanism for a Budget-Constrained Buyer

Contact Info

Product

Resources

About