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arxiv: 2408.01250 · v4 · submitted 2024-08-02 · 💰 econ.TH

Persuading an inattentive and privately informed receiver

Pietro Dall'Ara This is my paper

Pith reviewed 2026-05-23 22:38 UTC · model grok-4.3

classification 💰 econ.TH
keywords persuasioninformation designinattentionattention effortmechanism equivalencecensoringsupermodularity
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The pith

When receivers pay attention only at a cost, sender experiments become equivalent to direct persuasion mechanisms and optimally censor favorable states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines persuasion where the receiver processes new information only if she exerts costly effort. The sender designs an experiment that shapes both the chance the receiver pays attention and the action she ultimately chooses. The receiver's utility satisfies supermodularity between information and effort, meaning extra information is more valuable precisely when effort is high. This property delivers an equivalence between any experiment and a direct mechanism of the Kolotilin type. Applications then show that the sender's best experiment withholds some favorable information.

Core claim

By leveraging the supermodularity property of the receiver's utility in information and effort, the paper establishes an equivalence between experiments and persuasion mechanisms à la Kolotilin et al. (2017). In applications, the sender's optimal strategy involves censoring favorable states.

What carries the argument

supermodularity property in information and effort (the marginal value of information rises with effort), which maps experiments into equivalent direct mechanisms

Load-bearing premise

The receiver's utility is supermodular in information and effort; if this property fails the claimed equivalence between experiments and direct mechanisms no longer follows.

What would settle it

A concrete utility function violating supermodularity together with an optimal direct mechanism whose outcome cannot be replicated by any experiment that only varies the probability of attention.

Figures

Figures reproduced from arXiv: 2408.01250 by Pietro Dall'Ara.

Figure 1
Figure 1. Figure 1: An upper censorship (a) and a bi-upper censorship (b), for a state [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The timeline of the game. 2.2 Information and timing Information The state θ is distributed according to an atomless distribution F0 ∈ D, the prior belief, with mean x0, letting D be the set of distributions over [0, 1] identified by their distribution functions. The Receiver’s type is independent of θ and admits a marginal distribution of the attention type λ, G ∈ D, and a conditional distribution of the … view at source ↗
Figure 3
Figure 3. Figure 3: Panel (a) illustrates the set of information policies, panel (b) illustrates [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Panel (a) illustrates the construction of the net informativeness of infor [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The upper envelope J of the information policies in the persuasion mech￾anism I• = (I, L, K). We sketch the intuition and proof of Theorem 1, which leverage Corollary 1. The proof verifies that supermodularity is key by establishing the result for more general Receiver’s payoff functions (Appendix B.2). Let’s claim that the IC mechanism I• is equivalent to its upper envelope J ( [PITH_FULL_IMAGE:figures/f… view at source ↗
read the original abstract

This paper studies the persuasion of a receiver who accesses information only if she exerts costly attention effort. A sender designs an experiment to persuade the receiver to take a specific action. The experiment affects the receiver's attention effort, that is, the probability that she updates her beliefs. Persuasion has two margins: an extensive (effort) and an intensive (action). The receiver's utility exhibits a supermodularity property in information and effort. By leveraging this property, we establish an equivalence between experiments and persuasion mechanisms \`a la Kolotilin et al.~(2017). In applications, the sender's optimal strategy involves censoring favorable states.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper analyzes Bayesian persuasion where the receiver is privately informed and must exert costly effort to access the sender's experiment (i.e., attention is endogenous). The receiver's payoff is assumed supermodular in the precision of information received and the effort exerted. The central result is an equivalence between the design of experiments and direct persuasion mechanisms in the sense of Kolotilin et al. (2017). Applications of the equivalence are used to characterize the sender's optimum as involving censoring of favorable states.

Significance. If the equivalence result holds under the stated supermodularity condition, the paper provides a useful reduction that maps the problem with endogenous attention into a standard mechanism-design problem, extending the Kolotilin et al. framework to settings with inattentive receivers. This could facilitate analysis in applications where information processing is costly. The censoring result in applications is a concrete, testable implication.

minor comments (2)
  1. [Abstract and introduction] The abstract states that the equivalence 'follows from' supermodularity but does not indicate the precise steps (e.g., which direction of the equivalence uses which part of the supermodularity assumption). Adding a short proof sketch or reference to the relevant lemma in the main text would improve readability.
  2. [Section 3 (equivalence result)] The paper cites Kolotilin et al. (2017) for the direct-mechanism benchmark; it would be useful to clarify whether the equivalence preserves the same action space and whether any additional technical conditions (e.g., on the state space or action set) are inherited from that paper.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our paper and the recommendation for minor revision. The report correctly summarizes the main contribution—an equivalence between experiments and Kolotilin-style mechanisms under the supermodularity condition—and notes the concrete implications of the censoring result in applications.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper states an exogenous supermodularity property of the receiver's utility as a modeling assumption and leverages it to derive equivalence to mechanisms in Kolotilin et al. (2017). This is a standard conditional argument with no reduction of the central claim to a self-citation chain, fitted input renamed as prediction, or self-definitional step. The derivation remains independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the supermodularity assumption in the receiver's utility function and standard Bayesian persuasion setup; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Receiver's utility is supermodular in information and effort
    Invoked to obtain equivalence between experiments and mechanisms (abstract, paragraph 3)

pith-pipeline@v0.9.0 · 5620 in / 1262 out tokens · 34328 ms · 2026-05-23T22:38:52.948942+00:00 · methodology

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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages

  1. [1]

    and Kim C

    Aliprantis, Charalambos D. and Kim C. Border (2006), Infinite Dimensional Analysis: A Hitchhiker's Guide, third edition. Springer Berlin, Heidelberg. aliprantis_infinite_2006

    work page 2006

  2. [2]

    American Economic Review, 106(11), 3590–3605

    Alonso, Ricardo and Odilon C\^amara (2016), Persuading voters. American Economic Review, 106(11), 3590–3605. alonso_persuading_2016AER

    work page 2016

  3. [3]

    Theoretical Economics, 18(1), 15--36

    Arieli, Itai, Yakov Babichenko, Rann Smorodinsky, and Takuro Yamashita (2023), Optimal persuasion via bi-pooling. Theoretical Economics, 18(1), 15--36. arieli_optimal_2023

    work page 2023

  4. [4]

    Journal of Political Economy, 131(1), 202--245

    Au, Pak Hung and Mark Whitmeyer (2023), Attraction versus persuasion: Information provision in search markets. Journal of Political Economy, 131(1), 202--245. au_attraction_2023

    work page 2023

  5. [5]

    Barreto (2024), Persuading a wishful thinker

    Augias, Victor and Daniel M.\ A. Barreto (2024), Persuading a wishful thinker. Working Paper. augias_persuading_2023

    work page 2024

  6. [6]

    and Patrick L

    Bauschke, Heinz H. and Patrick L. Combettes (2011), Convex Analysis and Monotone Operator Theory in Hilbert Spaces, second edition. Springer Cham. bauschke_convex_2017

    work page 2011

  7. [7]

    Journal of Economic Theory, 179, 312--365

    Beauch\^ene, Dorian, Jian Li, and Ming Li (2019), Ambiguous persuasion. Journal of Economic Theory, 179, 312--365. beauchene_ambiguous_2019

    work page 2019

  8. [8]

    Journal of Economic Theory, 187, 105002

    Bizzotto, Jacopo, Jesper R\"udiger, and Adrien Vigier (2020), Testing, disclosure and approval. Journal of Economic Theory, 187, 105002. bizzotto_testing_2020

    work page 2020

  9. [9]

    American Economic Journal: Microeconomics, 13(2), 1–34

    Bizzotto, Jacopo and Adrien Vigier (2021), Fees, reputation, and information production in the credit rating industry. American Economic Journal: Microeconomics, 13(2), 1–34. bizzotto_fees_2021

    work page 2021

  10. [10]

    and Ilya Segal (2021), Persuading a Rationally Inattentive Agent

    Bloedel, Alexander W. and Ilya Segal (2021), Persuading a Rationally Inattentive Agent . Working Paper. bloedel_persuading_2021

    work page 2021

  11. [11]

    Journal of Political Economy, 126(5), 1965--2010

    Board, Simon and Jay Lu (2018), Competitive information disclosure in search markets. Journal of Political Economy, 126(5), 1965--2010. board_competitive_2018

    work page 2018

  12. [12]

    Marketing Science, 35(4), 605--618

    Branco, Fernando, Monic Sun, and J.\ Miguel Villas-Boas (2016), Too much information? information provision and search costs. Marketing Science, 35(4), 605--618. branco_too_2016

    work page 2016

  13. [13]

    Carrillo (2007), Influence through ignorance

    Brocas, Isabelle and Juan D. Carrillo (2007), Influence through ignorance. The RAND Journal of Economics, 38(4), 931--947. brocas_influence_2007

    work page 2007

  14. [14]

    Journal of Political Economy, 130(6), 1676--1715

    Caplin, Andrew, Mark Dean, and John Leahy (2022), Rationally inattentive behavior: Characterizing and generalizing shannon entropy. Journal of Political Economy, 130(6), 1676--1715. caplin_rationally_2022

    work page 2022

  15. [15]

    Journal of Political Economy, 131(7), 1797--1844

    Che, Yeon-Koo, Kyungmin Kim, and Konrad Mierendorff (2023), Keeping the listener engaged: A dynamic model of bayesian persuasion. Journal of Political Economy, 131(7), 1797--1844. che_keeping_2023

    work page 2023

  16. [16]

    Journal of Political Economy, 130(10), 2594--2642

    de Clippel, Geoffroy and Xu Zhang (2022), Non-bayesian persuasion. Journal of Political Economy, 130(10), 2594--2642. declippel_nonbayesian_2022

    work page 2022

  17. [17]

    American Economic Review, 112(10), 3215–59

    Denti, Tommaso (2022), Posterior separable cost of information. American Economic Review, 112(10), 3215–59. denti_posterior_2022

    work page 2022

  18. [18]

    American Economic Review, 112(9), 3106–23

    Denti, Tommaso, Massimo Marinacci, and Aldo Rustichini (2022), Experimental cost of information. American Economic Review, 112(9), 3106–23. denti_experimental_2022

    work page 2022

  19. [19]

    Journal of Political Economy, 127(5), 1993--2048

    Dworczak, Piotr and Giorgio Martini (2019), The Simple Economics of Optimal Persuasion . Journal of Political Economy, 127(5), 1993--2048. dworczak_simple_2019

    work page 2019

  20. [20]

    Econometrica, 90(5), 2017--2051

    Dworczak, Piotr and Alessandro Pavan (2022), Preparing for the worst but hoping for the best: Robust (bayesian) persuasion. Econometrica, 90(5), 2017--2051. dworczak_preparing_2022

    work page 2022

  21. [21]

    The Scandinavian Journal of Economics, 121(3), 1054--1087

    Felgenhauer, Mike (2019), Endogenous persuasion with costly verification. The Scandinavian Journal of Economics, 121(3), 1054--1087. felgenhauer_endogenous_2019

    work page 2019

  22. [22]

    In Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024 (David P

    Feng, Yiding, Chien - Ju Ho, and Wei Tang (2024), Rationality-robust information design: Bayesian persuasion under quantal response. In Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024 (David P. Woodruff, ed.), 501--546, SIAM . feng_rationalityrobust_2024

    work page 2024

  23. [23]

    Oxford University Press, Oxford

    Floridi, Luciano (2014), The Fourth Revolution : How the Infosphere is Reshaping Human Reality . Oxford University Press, Oxford. floridi_fourth_2014

    work page 2014

  24. [24]

    American Economic Review, 109(3), 996–1031

    Galperti, Simone (2019), Persuasion: The art of changing worldviews. American Economic Review, 109(3), 996–1031. galperti_persuasion_2019

    work page 2019

  25. [25]

    American Journal of Political Science, 59(1), 212--224

    Gehlbach, Scott and Alberto Simpser (2015), Electoral manipulation as bureaucratic control. American Journal of Political Science, 59(1), 212--224. gehlbach_electoral_2015

    work page 2015

  26. [26]

    Journal of Public Economics, 118, 163--171

    Gehlbach, Scott and Konstantin Sonin (2014), Government control of the media. Journal of Public Economics, 118, 163--171. gehlbach_government_2014

    work page 2014

  27. [27]

    American Economic Review, 106(5), 597--601

    Gentzkow, Matthew and Emir Kamenica (2016), A Rothschild - Stiglitz Approach to Bayesian Persuasion . American Economic Review, 106(5), 597--601. gentzkow_rothschild-stiglitz_2016

    work page 2016

  28. [28]

    Arda and Pooya Molavi (2023), Informational autocrats, diverse societies

    Gitmez, A. Arda and Pooya Molavi (2023), Informational autocrats, diverse societies. gitmez_informational_2023

    work page 2023

  29. [29]

    Econometrica, 87(2), 653--675

    Guo, Yingni and Eran Shmaya (2019), The interval structure of optimal disclosure. Econometrica, 87(2), 653--675. guo_interval_2019

    work page 2019

  30. [30]

    banking industry

    Honka, Elisabeth, Ali Horta c su, and Maria Ana Vitorino (2017), Advertising, consumer awareness, and choice: evidence from the u.s. banking industry. The RAND Journal of Economics, 48(3), 611--646. honka_advertising_2017

    work page 2017

  31. [31]

    ://arxiv.org/abs/2207.00685

    Hébert, Benjamin and Weijie Zhong (2024), Engagement maximization. ://arxiv.org/abs/2207.00685. hebert_engagement_2024

    work page arXiv 2024

  32. [32]

    Working Paper

    Jain, Vasudha and Mark Whitmeyer (2022), Competitive disclosure of information to a rationally inattentive agent. Working Paper. jain_competitive_2022

    work page 2022

  33. [33]

    Annual Review of Economics, 11, 249--272

    Kamenica, Emir (2019), Bayesian Persuasion and Information Design . Annual Review of Economics, 11, 249--272. kamenica_bayesian_2019

    work page 2019

  34. [34]

    American Economic Review, 101(6), 2590--2615

    Kamenica, Emir and Matthew Gentzkow (2011), Bayesian Persuasion . American Economic Review, 101(6), 2590--2615. kamenica_bayesian_2011

    work page 2011

  35. [35]

    Econometrica, 89(4), 1557--1593

    Kleiner, Andreas, Benny Moldovanu, and Philipp Strack (2021), Extreme Points and Majorization : Economic Applications . Econometrica, 89(4), 1557--1593. kleiner_extreme_2021

    work page 2021

  36. [36]

    Working Paper

    Knoepfle, Jan (2020), Dynamic competition for attention. Working Paper. knoepfle_dynamic_2020

    work page 2020

  37. [37]

    Theoretical Economics, 13(2), 607--635

    Kolotilin, Anton (2018), Optimal information disclosure: a linear programming approach. Theoretical Economics, 13(2), 607--635. kolotilin_optimal_2018

    work page 2018

  38. [38]

    Theoretical Economics, 17(2), 561--585

    Kolotilin, Anton, Timofiy Mylovanov, and Andriy Zapechelnyuk (2022), Censorship as optimal persuasion. Theoretical Economics, 17(2), 561--585. kolotilin_censorship_2022

    work page 2022

  39. [39]

    Econometrica, 85(6), 1949--1964

    Kolotilin, Anton, Tymofiy Mylovanov, Andriy Zapechelnyuk, and Ming Li (2017), Persuasion of a Privately Informed Receiver . Econometrica, 85(6), 1949--1964. kolotilin_persuasion_2017

    work page 2017

  40. [40]

    Journal of Mathematical Economics, 97, 102534

    Liao, Xiaoye (2021), Bayesian persuasion with optimal learning. Journal of Mathematical Economics, 97, 102534. liao_2021_bayesian

    work page 2021

  41. [41]

    American Economic Journal: Microeconomics, 10(4), 67--93

    Lipnowski, Elliot and Laurent Mathevet (2018), Disclosure to a psychological audience. American Economic Journal: Microeconomics, 10(4), 67--93. lipnowski_disclosure_2018

    work page 2018

  42. [42]

    American Economic Review: Insights, 2(1), 17--32

    Lipnowski, Elliot, Laurent Mathevet, and Dong Wei (2020), Attention management. American Economic Review: Insights, 2(1), 17--32. lipnowski_attention_2020

    work page 2020

  43. [43]

    Games and Economic Behavior, 133, 170--180

    Lipnowski, Elliot, Laurent Mathevet, and Dong Wei (2022), Optimal attention management: A tractable framework. Games and Economic Behavior, 133, 170--180. lipnowski_optimal_2022

    work page 2022

  44. [44]

    Working Paper

    Lipnowski, Elliot, Doron Ravid, and Denis Shishkin (2021), Persuasion via weak institutions. Working Paper. Electronic copy available at: https://ssrn.com/abstract=3168103, July 20, 2021. lipnowski_persuasion_2021

    work page 2021

  45. [45]

    lipnowski2024perfect

    Lipnowski, Elliot, Doron Ravid, and Denis Shishkin (2024), Perfect bayesian persuasion. lipnowski2024perfect

    work page 2024

  46. [46]

    (1982), Expected utility analysis without the independence axiom

    Machina, Mark J. (1982), Expected utility analysis without the independence axiom. Econometrica, 50(2), 277--324. machina_expected_1982

    work page 1982

  47. [47]

    Journal of Economic Theory, 211, 105678

    Matyskov\'a, Ludmila and Alfonso Montes (2023), Bayesian Persuasion With Costly Information Acquisition . Journal of Economic Theory, 211, 105678. matyskova_bayesian_2023

    work page 2023

  48. [48]

    Econometrica, 70(2), 583--601

    Milgrom, Paul and Ilya Segal (2002), Envelope theorems for arbitrary choice sets. Econometrica, 70(2), 583--601. milgrom_envelope_2002

    work page 2002

  49. [49]

    American Economic Review, 113(5), 1360–93

    Pomatto, Luciano, Philipp Strack, and Omer Tamuz (2023), The cost of information: The case of constant marginal costs. American Economic Review, 113(5), 1360–93. pomatto_cost_2023

    work page 2023

  50. [50]

    Journal of Political Economy, 118(5), 949--987

    Rayo, Luis and Ilya Segal (2010), Optimal Information Disclosure . Journal of Political Economy, 118(5), 949--987. rayo_optimal_2010

    work page 2010

  51. [51]

    Tyrell (1970), Convex Analysis

    Rockafellar, R. Tyrell (1970), Convex Analysis. Princeton University Press, Princeton. rockafellar_convex_1970

    work page 1970

  52. [52]

    American Economic Journal: Microeconomics, 11(2), 250–76

    Romanyuk, Gleb and Alex Smolin (2019), Cream skimming and information design in matching markets. American Economic Journal: Microeconomics, 11(2), 250–76. romanyuk_cream_2019

    work page 2019

  53. [53]

    Working Paper

    Shishkin, Denis (2024), Evidence Acquisition and Voluntary Disclosure . Working Paper. shishkin_evidence_2023

    work page 2024

  54. [54]

    (1996), Working paper no.\ 96--2 --- Knowledge and the time to attend to it

    Simon, Herbert A. (1996), Working paper no.\ 96--2 --- Knowledge and the time to attend to it. In Carnegie Bosch Institute for Applied Studies in International Management. simon_knowledge_1996

    work page 1996

  55. [55]

    (2003), Implications of rational inattention

    Sims, Christopher A. (2003), Implications of rational inattention. Journal of Monetary Economics, 50(3), 665--690. sims_implications_2003

    work page 2003

  56. [56]

    Working Paper

    Sun, Junze, Arthur Schram, and Randolph Sloof (2024), Publicly persuading voters: The single-crossing property and the optimality of interval revelation. Working Paper. sun_publicly_2024

    work page 2024

  57. [57]

    (1978), Minimizing a submodular function on a lattice

    Topkis, Donald M. (1978), Minimizing a submodular function on a lattice. Operations Research, 26(2), 305--321. topkis_minimizing_1978

    work page 1978

  58. [58]

    Marketing Science, 40(6), 1030--1058

    Tsai, Yi-Lin and Elisabeth Honka (2021), Informational and noninformational advertising content. Marketing Science, 40(6), 1030--1058. tsai_informational_2021

    work page 2021

  59. [59]

    Journal of Mathematical Economics, 94, 102451

    Wei, Dong (2021), Persuasion under costly learning. Journal of Mathematical Economics, 94, 102451. wei_persuasion_2021

    work page 2021

  60. [60]

    , " * write output.state after.block = add.period write newline

    ENTRY address annote author booktitle chapter edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.s...

    work page

  61. [61]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

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