Price discrimination through communication

Sher, Itai; Vohra, Rakesh

doi:10.3982/te1129

Cited by 35 publications

(15 citation statements)

References 31 publications

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“…However, the main focus of that paper is not on identifying the optimal mechanism as here, but rather on showing that some simple mechanisms are approximately optimal; to do so, it uses a simple but non-optimal choice of dual variables to obtain bounds on the optimal revenue. Other, earlier incarnations of our formula (4.9) appear in Sher and Vohra (2015), which gives a similar formula in a variant of a single-good monopoly problem, and Myerson (1991, Section 10.5), which studies a problem of welfare maximization with multiple agents and no transfers. 6 The present paper seems to be the first to use these generalized virtual values to characterize the exact optimum in a model of this generality.…”

Section: Related Multidimensional Screening Workmentioning

confidence: 89%

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Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

147

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: 89%

“…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%

Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

147

103

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“…The methodology of this paper is promising for various extensions of the persuasion scenario and also for a broader class of problems concerning mechanism design with evidence. 27 Sher and Vohra (2013) apply a similar methodology to the problem of optimal price discrimination on the basis of evidence, a problem that has strong ties to optimal auctions. That paper shows that the optimal price discrimination problem reduces to a minimum convex cost flow problem.…”

Section: Resultsmentioning

confidence: 99%

Persuasion and dynamic communication

Sher

2014

Theoretical Economics

Self Cite

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A speaker attempts to persuade a listener to accept a request by presenting evidence. A persuasion rule specifies what evidence is persuasive. This paper compares static and dynamic rules. We present a single linear program (i) whose solution corresponds to the listener's optimal dynamic rule and (ii) whose solution with additional integer constraints corresponds to the optimal static rule. We present a condition-foresight-under which the optimal persuasion problem reduces to the classical maximum flow problem. This has various qualitative consequences, including the coincidence of optimal dynamic and static persuasion rules, elimination of the need for randomization, and symmetry of optimal static rules. . I am grateful to Rakesh Vohra for suggesting the relation of the persuasion problem to the set cover problem. I thank Bart Lipman and two anonymous referees for their helpful comments. Shihui Ma, Nyalleng Moorosi, and Benjamin Segal provided valuable research assistance. I thank Kemal Badur for helping to construct the figures for this paper. A grant-in-aid and single semester leave from the University of Minnesota are gratefully acknowledged. All errors are mine.

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“…4 implementation literature (see, e.g., Green and Laffont (1986), Bull andWatson (2004, 2007), Deneckere and Severinov (2008), Sher andVohra (2011), Ben-Porath andLipman (2012), Kartik and Tercieux (2012)). 3 Uniqueness is assumed only in the Introduction to simplify the exposition.…”

mentioning

confidence: 98%

“…Our first main result characterizes the necessary and sufficient conditions for the existence of a fully revealing sequential equilibrium (Kreps and Wilson (1982)) when we restrict players to hold extremal beliefs off the equilibrium path, that is, beliefs that put probability 1 on a single type of a deviating player. 4 implementation literature (see, e.g., Green and Laffont (1986), Bull andWatson (2004, 2007), Deneckere and Severinov (2008), Sher and Vohra (2011), Ben-Porath and Lipman (2012), Kartik and Tercieux (2012)). 3 Uniqueness is assumed only in the Introduction to simplify the exposition.…”

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confidence: 99%

Certifiable Pre-Play Communication: Full Disclosure

2014

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This article asks when communication with certifiable information leads to complete information revelation. We consider Bayesian games augmented by a pre-play communication phase in which announcements are made publicly. We first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). Next, we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure. This characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in games with strategic complementarities, voting with deliberation, and persuasion games with multidimensional types

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Price discrimination through communication

Cited by 35 publications

References 31 publications

Robustness and Separation in Multidimensional Screening

Robustness and Separation in Multidimensional Screening

Persuasion and dynamic communication

Certifiable Pre-Play Communication: Full Disclosure

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