Optimal dynamic contracting: The first‐order approach and beyond

Battaglini, Marco; Lamba, Rohit

doi:10.3982/te2355

Cited by 32 publications

(28 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The survey of Rochet and Stole (2003, p. 150) (which also describes more applications) puts the point more forcefully: "In most cases that we can think of, a multidimensional preference parameterization seems critical to capturing the basic economics of the environment." In addition, there is a recent growth of interest in dynamic mechanism design, in which information arrives in each period; even if each period's information is single-dimensional, this field presents some of the same analytical challenges as static multidimensional mechanism design (Battaglini and Lamba (2015)).…”

Section: Introductionmentioning

confidence: 99%

Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

147

103

View full text Add to dashboard Cite

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

show abstract

Section: Introductionmentioning

confidence: 99%

Robustness and Separation in Multidimensional Screening

Carroll¹

2017

Econometrica

147

103

View full text Add to dashboard Cite

show abstract

“…Following now the same arguments as in Battaglini and Lamba (2017), I get the following Lemma, which differs only to their result by allowing for stochastic contracts.…”

Section: Optimal Contracting Under the First-order Approachmentioning

confidence: 82%

“…In recent years, there has been an increased interest in dynamic mechanism design, e.g. Courty and Li (2000), Battaglini (2005), Pavan et al (2009), Kapicka (2010), Gershkov and Perry (2012), Eső and Szentes (2013), Li and Shi (2013), Pavan et al (2014), Battaglini and Lamba (2017), Deb and Said (2015) and Krähmer and Strausz (2015) discuss this issue. All these papers, however, restrict to deterministic mechanisms accepting that this assumption is often with loss of generality.…”

Section: Introductionmentioning

confidence: 99%

Deterministic versus stochastic contracts in a dynamic principal-agent model

Mettral

2018

Econ Theory Bull

View full text Add to dashboard Cite

I show that deterministic dynamic contracts between a principal and an agent are always at least as profitable to the principal as stochastic ones, if the so-called first-order approach in dynamic mechanism design is satisfied. The principal commits, while the agent's type evolution follows a Markov process. My results demonstrate, even when allowing for potential correlation of stochastic contracts across periods that the usual restriction in the literature to deterministic contracts is admissible, as long as the first-order approach is valid.

show abstract

“…More generally, the paper relates to the literature on dynamic mechanism design, including Baron and Besanko (1984), Pavan, Segal and Toikka (2014), Bergemann and Välimäki (2010), Battaglini and Lamba (2015), Ata and Dana (2015), Garrett (2016), Garrett (2017), Ely, Garrett and Hinnosaar (2017), Gershkov, Moldovanu and Strack (2018). In contrast to the above papers, which feature dynamic information, Said (2012) and Board and Skrzypacz (2016) study models with a dynamic population of agents with fixed private information, where the designer can commit to a mechanism.…”

Section: Related Literaturementioning

confidence: 99%

Points Mechanisms and Rewards Programs

Temnyalov

2018

SSRN Journal

View full text Add to dashboard Cite

I study points programs, such as frequent flyer and other rewards programs, as a revenue management tool. I develop a two-period contracting model where a capacityconstrained firm faces consumers who privately learn their valuations over time. The firm cannot commit to long-term contracts, but it can commit to allocate any unsold capacity through a points program. This points scheme creates an endogenous and type-dependent outside option for consumers, which generates novel incentives in the firm's pricing problem. It induces the firm to screen less ex interim, and to offer lower equilibrium prices, reversing the intuition of demand cannibalization.

show abstract

Optimal dynamic contracting: The first‐order approach and beyond

Cited by 32 publications

References 45 publications

Robustness and Separation in Multidimensional Screening

Robustness and Separation in Multidimensional Screening

Deterministic versus stochastic contracts in a dynamic principal-agent model

Points Mechanisms and Rewards Programs

Contact Info

Product

Resources

About