Robustness of simple menus of contracts in cost-based procurement

Garrett, Daniel F.

doi:10.1016/j.geb.2013.06.004

Cited by 50 publications

(21 citation statements)

References 18 publications

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“…It is part of a growing body of work in robust mechanism design, seeking to explain intuitively simple mechanisms as providing guaranteed performance in uncertain environments, and formalizing this intuition by showing how such mechanisms can arise as solutions to worst-case optimization problems. This examination includes earlier work by this author on contracting problems in uncertain environments (Carroll (2015a(Carroll ( , 2015b, Carroll and Meng (2016)), as well as several others (Bergemann and Morris (2005), Brooks (2013), Chung and Ely (2007), Frankel (2014), Garrett (2014)). It also relates to a recent spurt of interest in multidimensional screening, particularly in the algorithmic game theory world.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

156

103

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“…This paper is part of a growing literature on robust contracting in an uncertain environment, which includes work on procurement contracts (Garrett 2014), optimal delegation mechanisms (Frankel 2014;Carrasco and Moreira 2013), and optimal incentive contracts in the presence of moral hazard (Carroll 2015;Carroll and Meng 2016;Antić 2014). Crucially, and in contrast to most prior work in mechanism design, the principal in these models evaluates contracts according to their worst-case performance, e.g., over the agent's preferences or over the set of available technologies.…”

Section: Related Literaturementioning

confidence: 99%

Robust contracting under common value uncertainty

Auster

2018

Theoretical Economics

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A buyer makes an offer to a privately informed seller for a good of uncertain quality. Quality determines both the seller's valuation and the buyer's valuation, and the buyer evaluates each contract according to its worst-case performance over a set of probability distributions. This paper demonstrates that the contract that maximizes the minimum payoff over all possible probability distributions of quality is a screening menu that separates all types, whereas the optimal contract for any given probability distribution is a posted price, which induces bunching. Using the ε-contamination model, according to which the buyer's utility is a weighted average of his single prior expected utility and the worst-case scenario, the analysis further shows that for intermediate degrees of confidence, the optimal mechanism combines features of both of these contracts. the participants of various seminars for very helpful comments.

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“…This, in turn, allows for more general mechanisms than the "delegation" ones those papers derive. Garrett (2014) considers the case of a principal who does not know the producer's disutility of effort, and shows that a simple fixed-price-cost-reimbursement (FPCR) menu minimizes the principal's maximum expected payment to the agent. In Carroll (2015a), the principal only partially knows the set of actions available to the agent; he shows that if the principal maximizes expected profits under worst-case set of actions, the optimal contract is linear in output.…”

Section: Related Literaturementioning

confidence: 99%

Robust Mechanisms: The Curvature Case

et al. 2017

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis note considers the problem of a principal (she) who faces a privately informed agent (he) and only knows one moment of the distribution from which his types are drawn.Payoffs are non-linear in the allocation and the principal maximizes her worst-case expected profits. We recast the robust design problem as a zero-sum game played by the principal and an adversarial nature who seeks to minimize her expected payoffs. The robust mechanism and the worst case distribution are, then, the Nash equilibrium of such game. A robustness property of the optimal mechanism imposes restrictions on the principal's ex-post profit function. These restrictions then lead to the optimal mechanism. The robust mechanism entails exclusion of low types and distortions at the intensive margin that (in a precise sense)are larger than what those that prevail in standard Bayesian mechanism design problems. D86 (Economics of Contract Theory) * This note is being extended to incorporate two sets of analysis: (i) a dynamic version of the main model in which the agent's information evolves over time and all is known by the principal is that types satisfy a martingale condition, and (ii) a multidimensional version of the model. We are also working on the full derivation of examples (e.g., regulation and taxation) that use the results this work derives. A paper incorporating (i), (ii) and the examples will subsume this note.† We have benefited from conversations with Gabriel Carroll, Nicolás Figueroa, Stephen Morris, Leonardo Rezende and Yuliy Sannikov. Moreira gratefully acknowledges financial support from CNPq.

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Robustness of simple menus of contracts in cost-based procurement

Cited by 50 publications

References 18 publications

Robustness and Separation in Multidimensional Screening

Robustness and Separation in Multidimensional Screening

Robust contracting under common value uncertainty

Robust Mechanisms: The Curvature Case

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