Mechanism Design with Limited Commitment

Doval, Laura; Skreta, Vasiliki

doi:10.48550/arxiv.1811.03579

Cited by 3 publications

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“…From a methodological perspective, our paper contributes to the literature on mechanism design with limited commitment, by considering a setting where (i) the consumer's private information in the first period is drawn from a continuum, and (ii) whereas the consumer's private information is positively correlated across periods, it is not fully persistent. This is possible thanks to the results in Doval and Skreta (2020), who provide a revelation principle for environments such as those analyzed in this paper.…”

Section: Preview Of Resultsmentioning

confidence: 88%

“…For reasons similar to those in Laffont and Tirole (1988), to derive the optimal mechanism under limited commitment, we cannot rely on the revelation principle (see, e.g., Myerson, 1986). Instead, we rely on Theorem 2 in Doval and Skreta (2020), which provides a revelation principle for limited commitment in Markov environments, like the one we consider in this paper. 5 As we explain in Section 4, Theorem 2 in Doval and Skreta (2020) allows us to reduce the search for the firm's optimal mechanism to a constrained optimization program.…”

Section: Preview Of Resultsmentioning

confidence: 99%

“…Instead, we rely on Theorem 2 in Doval and Skreta (2020), which provides a revelation principle for limited commitment in Markov environments, like the one we consider in this paper. 5 As we explain in Section 4, Theorem 2 in Doval and Skreta (2020) allows us to reduce the search for the firm's optimal mechanism to a constrained optimization program. In particular, by leveraging the analysis in Doval and Skreta (2020), we construct the firm's optimal product line by marrying elements of mechanism design and information design.…”

Section: Preview Of Resultsmentioning

confidence: 99%

“…5 As we explain in Section 4, Theorem 2 in Doval and Skreta (2020) allows us to reduce the search for the firm's optimal mechanism to a constrained optimization program. In particular, by leveraging the analysis in Doval and Skreta (2020), we construct the firm's optimal product line by marrying elements of mechanism design and information design. On the mechanism design side, we leverage the first order approach in dynamic mechanism design and dynamic public finance to characterize the solution to a relaxed problem and then provide conditions under which the firm can implement the solution to the relaxed problem (see Pavan et al, 2014;Stantcheva, 2020).…”

Section: Preview Of Resultsmentioning

confidence: 99%

“…To characterize the optimal mechanism under limited commitment, we proceed in two steps. First, we apply Theorem 2 in Doval and Skreta (2020). This allows us to restrict the search for the firm's optimal PBE to a well-defined set of mechanisms for the firm and to simple strategies for the consumer.…”

Section: Product-line Design Under Limited Commitmentmentioning

confidence: 99%

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Purchase history and product personalization

Doval¹,

Skreta²

2021

Preprint

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Product personalization opens the door to price discrimination. A rich product line allows for higher consumer satisfaction, but the mere choice of a product carries valuable information about the consumer that the firm can leverage for price discrimination. Controlling the degree of product personalization provides the firm with an additional tool to curb ratcheting forces arising from consumers' awareness of being price discriminated. Indeed, a firm's inability to not engage in price discrimination introduces a novel distortion: The firm offers a subset of the products that it would offer if, instead, the firm could commit to not price discriminate. Doing so gives commitment power to the firm: By 'pooling' consumers with different tastes to the same variety the firm commits not to learn their tastes.

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Section: Preview Of Resultsmentioning

confidence: 88%

Section: Preview Of Resultsmentioning

confidence: 99%

Section: Preview Of Resultsmentioning

confidence: 99%

Section: Preview Of Resultsmentioning

confidence: 99%

Section: Product-line Design Under Limited Commitmentmentioning

confidence: 99%

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Purchase history and product personalization

Doval¹,

Skreta²

2021

Preprint

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Optimal Mechanism for the Sale of a Durable Good

Doval

Skreta

2019

SSRN Journal

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We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer's truthtelling and participation constraints, the seller's problem is a decision problem, in the case of limited commitment, the seller's problem corresponds to an intrapersonal game, where different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation. Pollak (1968). Our contribution to this literature is to show that optimal mechanisms under limited commitment can be obtained as a solution to an intrapersonal game, even when both the seller and the buyer have time consistent preferences. In this way, we extend the range of applications of this literature, which has already seen applications ranging from growth and development (Bernheim et al. (2015)) to saving decisions (Harris and Laibson (2001)).Organization The rest of the paper is organized as follows. Section 2 describes the model; Section 2.1 summarizes the results in Doval and Skreta (2018) used to simplify the analysis that follows. Section 3 formally states the main result and describes the main steps in the proof of Theorem 1. Section 3.1 derives the recursive formulation that is the basis of the intrapersonal game; Section 3.2 characterizes the unique equilibrium of the intrapersonal game; Section 3.3 uses the intrapersonal equilibrium to build a PBE assessment that delivers the revenue-maximizing PBE. Section 4 concludes. ModelPrimitives: Two players, a seller and a buyer, interact over infinitely many periods. The seller owns one unit of a durable good to which he attaches value 0. The buyer has private information: before her interaction with the seller starts, she observes her valuation v ∈ {v L , v H } ≡ V, with 0 ≤ v L < v H . Let µ 0 denote the probability that the buyer's valuation is v H at the beginning of the game. In what follows, we denote by ∆(V) the set of distributions on V.An allocation in period t is a pair (q, x) ∈ {0, 1} × R, where q indicates whether the good is traded (q = 1) or not (q = 0), and x is a payment from the buyer to the seller. The game ends the first time the good is traded.Payoffs are as follows. If in period t, the allocation is (q, x), the flow payoffs are u B (q, x, v) = vq − x and u S (q, x) = x for the buyer and the seller, respectively. The seller and the buyer maximize the expected discounted sum of flow payoffs. They share a common discount factor δ ∈ (0, 1). Mechanisms:To introduce the timing of the game, we first define the action space of the seller in each period. In each period, the seller offers the buyer a mech-3. µ(h t ) is derived via Bayes' rule where possible (see Definition 4 in Section A.1). 10 9 While there is no output message when the buyer does not participate in the mechanism, we denote this by s = ∅ to keep the length...

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Slow persuasion

Escudé

Sinander

2023

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What are the value and form of optimal persuasion when information can be generated only slowly? We study this question in a dynamic model in which a “sender” provides public information over time subject to a graduality constraint, and a decision maker takes an action in each period. Using a novel “viscosity” dynamic programming principle, we characterize the sender's equilibrium value function and information provision. We show that the graduality constraint inhibits information provision relative to unconstrained persuasion. The gap can be substantial, but closes as the constraint slackens. Contrary to unconstrained persuasion, less‐than‐full information may be provided even if players have aligned preferences but different prior beliefs.

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Mechanism Design with Limited Commitment

Cited by 3 publications

References 0 publications

Purchase history and product personalization

Purchase history and product personalization

Optimal Mechanism for the Sale of a Durable Good

Slow persuasion

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