A duality-based unified approach to Bayesian mechanism design

Cai, Yang; Devanur, Nikhil R.; Weinberg, S. Matthew

doi:10.1145/2994501.2994506

Cited by 81 publications

(376 citation statements)

References 60 publications

(126 reference statements)

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“…The concept of generalized virtual values, central to this paper, does have antecedents in the literature. Most closely related is the independent and simultaneous work of Cai, Devanur, and Weinberg (2016). That paper gives essentially the same definition (4.9) for generalized virtual values and proves Lemma 4.1 (both parts).…”

Section: Related Multidimensional Screening Workmentioning

confidence: 64%

“…The papers by Sher and Vohra (2015) and Cai, Devanur, and Weinberg (2016) also walk through the connection with traditional single-good virtual values, just as we describe in the Supplemental Material, and these two papers introduce the "flow conservation" terminology, which we have followed here.…”

Section: Related Multidimensional Screening Workmentioning

confidence: 99%

“…Several recent papers in this area have given conditions under which simple mechanisms can be shown to be optimal (Haghpanah and Hartline (2015), Wang and Tang (2014)); most relevant among these, Haghpanah and Hartline (2015) introduce a virtual value maximization approach that is connected to ours. Others (Hart and Nisan (2012), Li and Yao (2013), Babaioff et al (2014), Rubinstein and Weinberg (2015), Yao (2015), Cai, Devanur, and Weinberg (2016)) have argued that simple mechanisms for selling multiple goods are approximately optimal under broad conditions. Finally, there is a longstanding, more applied literature on bundling in industrial organization (Stigler (1963), Adams and Yellen (1976), McAfee, McMillan, and Whinston (1989), Chu, Leslie, and Sorensen (2011)), to which we shall return periodically.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the concept of generalized virtual values, a key analytical tool here, appears to be relatively new to the literature, even though it falls out straightforwardly from the Lagrangian of the principal's maximization problem. (Cai, Devanur, and Weinberg (2016) independently introduce this same concept. )…”

Section: Introductionmentioning

confidence: 99%

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Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

156

103

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This supplement contains additional materials for the main paper. Section B contains proofs of auxiliary results not included in the main paper. Section C details how the generalized virtual values coincide with traditional (ironed) virtual values in the single-good monopoly problem. Theorems, equations, and sections in the main paper are referenced using the original numbering.APPENDIX B: ADDITIONAL PROOFS PROOF OF LEMMA 4.3 (ADAPTED FROM MADARÁSZ AND PRAT (2012)): It is easy to see that statement (b) of the lemma follows from (a) by integrating over each S k in the partition; so it suffices to prove (a).As in the proof of Lemma 4.2, we can take = max x θ u(x θ) − min x θ u(x θ), and then in any mechanism, any two types' payments can differ by at most . Also, put τ = min{ε/6 1}.By Lipschitz continuity, there exists δ such that whenever θ θ are two types with d(θ θ ) < δ, then |u(x θ) − u(x θ )| < τε/6 for all x. We show this δ has the desired property.Let (x t) be any given mechanism. Let t = min θ t(θ). Let S ⊆ (X) × R be the set of values (x(θ) τt + (1 − τ)t(θ)) for θ ∈ Θ and let S be its closure, which is compact (by the above observation on payments). Then define ( x t) by simply assigning to each type θ ∈ Θ the outcome in S that maximizes its payoff, Eu(x θ) − t. This exists by compactness. This ( x t) is a mechanism: IC is satisfied by definition and IR is satisfied since the payments have only been reduced relative to those in (x t), so each type θ has the option of getting allocation x(θ) for a payment of less than t(θ), which gives nonnegative payoff. Now let d(θ θ ) < δ. We know that the outcome chosen by θ in the new mechanism can be approximated arbitrarily closely by an element of S corresponding to some type θ ; in particular, there exists θ such that Eu x θ θ − Eu x θ θ < τε 6 and t θ − τt + (1 − τ)t θ < τε 6 (B.1) Now, we know from IC for the original mechanism thatand by the definition of the new mechanism ( x t) that Eu x θ θ − t θ ≥ Eu x(θ) θ − τt + (1 − τ)t(θ)Using (twice) the fact that d(θ θ ) < δ, the latter inequality turns into Eu x θ θ − t θ ≥ Eu x(θ) θ − τt + (1 − τ)t(θ) − τε 3

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Section: Related Multidimensional Screening Workmentioning

confidence: 64%

Section: Related Multidimensional Screening Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

156

103

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“…A major contribution of theoretical computer science to game theory and economics has been the articulation of natural classes of succinctly representable settings and a thorough study of the computational complexity of optimal design problems in such settings. Examples include work on multi-dimensional mechanism design that has emphasized succinct type distributions [9,10,11,12], succinct signalling schemes with an exponential number of states of nature [20], and the efficient computation of correlated equilibria in succinctly representable multi-player games [46,36]. The goal of this paper is to initiate an analogous line of work for succinctly described agency problems in contract theory.…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Contracts

Dütting¹,

Roughgarden²,

Cohen³

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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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 "firstbest" (full-welfare-extracting) solution, and that such a contract can be computed in polynomial time.

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