Is Selling Complete Information (Approximately) Optimal?

Bergemann, Dirk; Cai, Yang; Grigoris, Velegkas,; Zhao, Mingfei

doi:10.1145/3490486.3538304

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…More generally, our work relates to the problem of how to sell payoff-relevant hard information to a potential buyer. Bergemann et al (2018) solve for the revenue-maximizing mechanism in binary environments, and Bergemann et al (2022) establish when full disclosure is approximately optimal under more general spaces of actions. In contrast, our certifying agent is selling a signal that is valuable in that it conveys information to other participants in a subsequent game.…”

Section: Related Literaturementioning

confidence: 99%

Certification Design for a Competitive Market

A.¹,

Immorlica²,

Lucier³

2023

Preprint

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Motivated by applications such as voluntary carbon markets and educational testing, we consider a market for goods with varying but hidden levels of quality in the presence of a third-party certifier. The certifier can provide informative signals about the quality of products, and can charge for this service. Sellers choose both the quality of the product they produce and a certification. Prices are then determined in a competitive market. Under a single-crossing condition, we show that the levels of certification chosen by producers are uniquely determined at equilibrium. We then show how to reduce a revenue-maximizing certifier's problem to a monopolistic pricing problem with non-linear valuations, and design an FPTAS for computing the optimal slate of certificates and their prices. In general, both the welfare-optimal and revenue-optimal slate of certificates can be arbitrarily large.

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Section: Related Literaturementioning

confidence: 99%

Certification Design for a Competitive Market

A.¹,

Immorlica²,

Lucier³

2023

Preprint

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“…The problem of selling information has also been addressed by Bergemann et al (2018), who study the case of binary actions and states of nature, characterizing a revenue-maximizing mechanism in such a setting. Furthermore, Bergemann et al (2022) extend the analysis to the case in which there are more than two actions and binary states of nature. In contrast, Liu et al (2021) study a revenue-maximizing mechanism for selling information when the stochasticity of the state of nature only affects a subset of the actions of the decision maker.…”

Section: Related Workmentioning

confidence: 99%

Selling Information while Being an Interested Party

Castiglioni¹,

Bacchiocchi²,

Marchesi³

et al. 2023

Preprint

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We study the algorithmic problem faced by an information holder (seller) who wants to optimally sell such information to a budged-constrained decision maker (buyer) that has to undertake some action. Differently from previous works addressing this problem, we consider the case in which the seller is an interested party, as the action chosen by the buyer does not only influence their utility, but also seller's one. This happens in many real-world settings, where the way in which businesses use acquired information may positively or negatively affect the seller, due to the presence of externalities on the information market. The utilities of both the seller and the buyer depend on a random state of nature, which is revealed to the seller, but it is unknown to the buyer. Thus, the seller's goal is to (partially) sell their information about the state of nature to the buyer, so as to concurrently maximize revenue and induce the buyer to take a desirable action.We study settings in which buyer's budget and utilities are determined by a random buyer's type that is unknown to the seller. In such settings, an optimal protocol for the seller must propose to the buyer a menu of information-revelation policies to choose from, with the latter acquiring one of them by paying its corresponding price. Moreover, since in our model the seller is an interested party, an optimal protocol must also prescribe the seller to pay back the buyer contingently on their action.First, we show that the problem of computing a seller-optimal protocol can be solved in polynomial time. This result relies on a quadratic formulation of the problem, which we solve by means of a linear programming relaxation. Next, we switch the attention to the case in which a seller's protocol employs a single information-revelation policy, rather than proposing a menu. In such a setting, we show that computing a seller-optimal protocol is APX-hard, even when either the number of actions or that of states of nature is fixed. We complement such a negative result by providing a quasipolynomial-time approximation algorithm that, given any ρ > 0 and ǫ > 0 as input, provides a multiplicative approximation ρ of the optimal seller's expected utility, by only suffering a negligible 2 −Ω(1/ρ) + ǫ additive loss. Such an algorithm runs in polynomial time whenever either the number of buyer's actions or that of states of nature is fixed. In order to derive our results, we draw a connection between our information-selling problem and principal-agent problems with observable actions. Finally, we complete the picture of the computational complexity of finding seller-optimal protocols without menus by providing additional results for the specific setting in which the buyer has limited liability, and by designing a polynomial-time algorithm for the case in which buyer's types are fixed.

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Is Selling Complete Information (Approximately) Optimal?

Cited by 2 publications

References 18 publications

Certification Design for a Competitive Market

Certification Design for a Competitive Market

Selling Information while Being an Interested Party

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