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Is Selling Complete Information (Approximately) Optimal?
Computer Science and Game Theory · Submitted 18 Feb 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the environment with binary state and $m\geq 3$ actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor.
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The abstract, sentence by sentence
We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by [Blackwell, 1951, 1953]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. [Bergemann et al., 2018] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and $m\geq 3$ actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. | background 0.63 | 0.77 | 0.02 | asserted 0.75 |
| s1 | We consider the classic Bayesian decision-theoretic model pioneered by [Blackwell, 1951, 1953]. | background 1.00 | 0.07 | 0.01 | asserted 0.98 |
| s2 | Initially, the data buyer has only partial information about the payoff-relevant state of the world. | background 1.00 | 0.06 | 0.01 | asserted 1.00 |
| s3 | A data seller offers additional information about the state of the world. | background 1.00 | 0.07 | 0.01 | asserted 0.98 |
| s4 | The information is revealed through signaling schemes, also referred to as experiments. | background 0.93 | 0.06 | 0.01 | asserted 1.00 |
| s5 | In the single-agent setting, any mechanism can be represented as a menu of experiments. | background 0.99 | 0.09 | 0.02 | asserted 1.00 |
| s6 | [Bergemann et al., 2018] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. | background 0.97 | 0.03 | 0.02 | asserted 1.00 |
| s7 | By contrast, no characterization is known for the case with more actions. | gap 1.00 | 0.05 | 0.03 | asserted 0.99 |
| s8 | In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. | contribution 0.97 | 0.64 | 0.07 | asserted 0.82 |
| s9 | In the environment with binary state and $m\geq 3$ actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. | result 0.96 | 0.96 | 0.64 | asserted 1.00 |
| s10 | An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. | interpretation 0.63 | 0.91 | 0.16 | asserted 1.00 |
| s11 | For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. | result 0.99 | 0.94 | 0.17 | asserted 1.00 |
| s12 | Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism. | result 1.00 | 0.94 | 0.13 | asserted 1.00 |
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The paper
Original abstract
We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by [Blackwell, 1951, 1953]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. [Bergemann et al., 2018] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and $m\geq 3$ actions, we provide an $O(m)$-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.
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How the literature uses it
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What it cites
Cites as background 2 papers
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Complete characterizations are known only in several special cases [ref] .
Optimal Mechanism Design for Single-Minded Agents · Additional Related Work · 0.84
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A recent paper by Li [ref] studies the case where the agent has endogenous information, meaning that she can perform her own experiment at a certain cost after receiving the signal.
Selling Data to an Agent with Endogenous Information · Additional Related Work · 0.84
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