Pith. sign in

REVIEW 1 major objections 3 minor 114 references

Information Aggregation and Social Networks: Responsiveness and Overturning

T0 review · 1 major / 3 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read No single network structure is uniformly optimal for social learning.

desk verdict Solid paper with a fixable but real gap: Corollary 1 is false for N=2 because star and complete networks coincide; the intended N≥3 result is probably right. read the letter →

arxiv 2607.28921 v1 pith:NLKOL45S submitted 2026-07-31 econ.TH

Shinpei Noguchi , Hiroto Sato , Konan Shimizu This is my paper
classification econ.TH MSC 91B4491D30
keywords sociallearningsequentialnetworkstructureinformationaggregationcascadesresponsivenesseffectoverturningstar
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether some observation network — who watches whose past actions — is always the best way to aggregate dispersed private information in a sequential social-learning model. It proves the answer is no. Under one binary signal structure, the star network (everyone acts independently, then the last agent sees all actions) strictly beats every other network. Under a different four-signal structure, the complete network (everyone sees all past actions) strictly beats every other network. Therefore no network dominates across all information structures; which network wins depends on whether preserving private responsiveness or enabling overturning of bad public beliefs matters more.

What carries the argument

The two extreme networks: the star network, where all but the last agent act on private signals alone and the last agent observes everyone; and the complete network, where every agent observes all earlier actions. The proof machinery is a pair of constructed information structures and the two forces they isolate. The responsiveness effect: less connected networks keep actions sensitive to private signals, avoiding cascades. The overturning effect: fully connected networks let an action that reverses the prevailing history reveal that its agent received an unusually informative signal, and later agents can read that reversal. The four-signal structure in Theorem 2 has likelihood ratios ordere

What would settle it

Compute, for the constructed four-signal structure Π*, the equilibrium payoffs of the complete network versus every other network for N=4; if any non-complete network matched or exceeded the complete network's terminal payoff, Theorem 2 would fail. More directly, to falsify Corollary 1 one would need a network that is weakly best under both Π_B and Π*, which the uniqueness proofs forbid.

Watch

Extended reading notes

Core claim

The central discovery is a negative result about network rankings: for the criterion of the terminal agent's expected payoff at a fixed finite period, there is no network that weakly outperforms every other network for every information structure. The proof is by constructing two opposite information structures. Theorem 1 builds a binary information structure in which, because actions perfectly reveal binary signals, the star network makes every predecessor's signal directly readable, whereas any connected network induces cascades that destroy responsiveness; hence star uniquely maximizes the last agent's payoff. Theorem 2 builds a four-signal structure with lexicographically ordered informa

Load-bearing premise

The 'no uniform optimum' conclusion is established only when we evaluate networks by the expected payoff of the last decision-maker at a single fixed finite period; if the objective were long-run learning speed or average welfare of all agents, a uniformly best network could still exist.

Editorial extensions

If this is right

  • For any fixed information structure, the best network must be evaluated jointly with the signal distribution; no off-the-shelf ranking of networks exists.
  • In environments where moderately informative signals dominate, sacrificing a few early agents to act independently (star-like 'guinea pig' design) improves terminal decisions.
  • In environments where extremely informative signals occur with nontrivial probability, full transparency of histories (complete-network-like design) lets one surprising action correct a long wrong chain.
  • The trade-off persists in large societies: as the number of agents grows, both networks achieve asymptotic learning, but the rate comparison still depends on the same cutoff.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The non-uniformity result is proven for the terminal agent's expected payoff at a finite horizon; a different welfare criterion such as utilitarian average payoff or long-run learning speed might in principle admit a uniformly best network, and this paper does not rule that out.
  • One could test the trade-off empirically in laboratory settings: vary the tail-thickness of signal distributions and compare whether allowing subjects to observe all previous actions versus isolating them changes accuracy in the direction predicted.
  • The overturning effect suggests a design principle for platforms: when signals can be extreme but rare, making reversals salient (e.g., highlighting action switches) may substitute for full network connectivity.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 3 minor

Summary. The paper studies sequential social learning in a finite-horizon model with binary actions and a uniform prior. Two extreme networks are analyzed: a star network, in which only the terminal agent observes all predecessors, and a complete network, in which every agent observes all predecessors. Theorem 1 constructs a binary signal structure under which the star network uniquely maximizes the terminal agent's expected payoff, and Theorem 2 constructs a four-signal information structure under which the complete network uniquely maximizes it. The paper concludes (Corollary 1) that no network is uniformly optimal across all information structures. Section 5 provides a cutoff characterization in a mixture-of-binary-and-conclusive-signals class and numerical support. The proofs are collected in appendices.

Significance. The main conceptual message — that the ranking of networks depends on the information structure, so denser observation is not uniformly better — is interesting and, once the N≥3 scope is made explicit, is supported by a careful analysis. The construction underlying Theorem 2, with lexicographically ordered signal likelihoods that make overturning histories interpretable, is a novel technique and is verified through the inequalities in Lemma 3. Proposition 2 gives a sharp, falsifiable comparative static with an explicit limit as N→∞. The paper does not estimate parameters from data and does not rely on its own prior results. The welfare criterion is transparent: the main theorems concern the terminal agent's expected payoff at a fixed finite horizon, with Proposition 1 extending the complete-network advantage to all agents under the constructed information structure.

major comments (1)
  1. [Section 3; Definitions 1–2; Corollary 1; Appendix C.3] The model allows N=2 (Section 3), but for N=2 Definitions 1 and 2 coincide: both give N_2={1}, and the only other network has N_2=∅. By Lemma 1 (Appendix A.2), V_2(full,Π) ≥ V_2(empty,Π) for every information structure Π. Hence the full network satisfies the uniform-optimality condition in Corollary 1, directly contradicting the corollary as stated. The proof after Theorem 2 requires star≠complete to obtain a contradiction, which fails when N=2. The proof of Theorem 2 in Appendix C.3 also does not handle this case: after the Lemma 1 reduction, the constructed network for an N=2 non-complete network is the complete network itself, so neither Condition (I) nor (II) is violated and Lemma 8(iii) does not apply because N=N_C. The fix is local but load-bearing: state Theorems 1, 2, and Corollary 1 for N≥3 (or add an explicit N=2 exception to Corollary 1). Proposition 2 already restricts to N≥3
minor comments (3)
  1. [Appendix C.1] The text states LR(l*)=δ^{N^3}, but from the definitions π*(l*|L)=δ^{α+1} and π*(l*|H)=δ^{(α+1)N^3}, the correct value is LR(l*)=δ^{(α+1)(N^3-1)}. The proofs in Lemma 3 use the correct value, so this is a typo, but it should be corrected.
  2. [Section 4] The paragraph beginning 'However, analyzing the general properties of how connectivity affects agents' payoffs is highly complicated... Given this difficulty, we focus on two important networks...' is repeated almost verbatim two paragraphs in a row. One copy should be removed.
  3. [Appendix B, proof of Lemma 3] In the proof of inequality (1), the sentence 'the second inequality follows from δ<1/(3N)<1/3' appears to refer to the third inequality in the displayed chain. Please clarify the reference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the existence results are self-contained constructions with no fitted parameters and no load-bearing self-citations.

full rationale

The paper's central claims, Theorems 1 and 2, are existence results established by explicitly constructed information structures. Theorem 1 fixes a binary information structure satisfying LR(l)LR(h)^{N-2}<1<LR(l)LR(h)^{N-1} and proves, via Lemma 2, that the star network uniquely maximizes agent N's expected payoff. Theorem 2 constructs a four-signal information structure Pi* using an auxiliary parameter delta in (0,1/(3N)), proves the required likelihood-ratio inequalities in Lemma 3, characterizes equilibrium actions in Lemmas 4-6, and then proves strict optimality of the complete network. Corollary 1 is a direct logical consequence of Theorems 1 and 2: a uniformly optimal network would have to coincide with the star network under Pi_B and with the complete network under Pi*, and since these networks differ for N>=3, no such network exists. No parameter is estimated from data, no prediction is a renamed fitted value, and no step relies on the authors' own prior work. The self-citation pattern is absent: citations to Ali, Smith-Sorensen, and the classical cascades literature are contextual and non-load-bearing. One non-circular correctness concern is that the model allows N=2, where the star and complete networks coincide, making Corollary 1 false as stated; however, this is a boundary-case correctness issue, not circularity, since the proof itself does not presuppose its conclusion. The numerical exercises in Section 5.2 also compare closed-form expected payoffs under fixed families of distributions rather than fitting parameters and relabeling them as predictions. Overall, the derivation chain is self-contained and no circular step is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The main theorems use only standard Bayesian updating and the constructed information structures. The only ad hoc numeric is the auxiliary δ in Theorem 2; there are no fitted parameters and no newly postulated physical or economic entities.

free parameters (1)
  • δ (auxiliary construction parameter for Π*) = any δ ∈ (0, 1/(3N))
    Introduced in Appendix C to satisfy the inequalities of Lemma 3. The payoff comparison is robust to the exact value; it is a proof device, not a fitted quantity.
assumptions (5)
  • domain assumption Common prior with P(H)=P(L)=1/2
    Model section: 'The prior is assumed to assign equal probability to each state.' Used throughout in payoff and likelihood calculations.
  • domain assumption Private signals are conditionally independent and identically distributed across agents
    Model section: 'each agent receives a private signal ... (independently) drawn from the information structure.' This independence is used for the product structure Π^{⊗i} and the binomial calculations in Proposition 2.
  • domain assumption Agents observe only neighbors' actions, not private signals
    Model section: 'agent i first observes the (partial) history, consisting of the actions of agents in N_i.' This is the core information channel that makes network structure matter.
  • ad hoc to paper Tie-breaking rule: indifferent agents choose action 0
    Model section: 'whenever an agent is indifferent between the two actions in terms of expected payoff, the agent chooses action 0.' This pins down a unique equilibrium; the constructed information structures use strict inequalities so the main theorems do not hinge on the rule, but it is an explicit modeling choice.
  • domain assumption Payoff is 1 if action matches the state, 0 otherwise
    Model section: 'u(a,θ)=1 if (a,θ)=(0,L) or (1,H) and u(a,θ)=0 otherwise.' This symmetric payoff structure is used in all expected-payoff comparisons.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Information Aggregation and Social Networks: Responsiveness and Overturning." pith.science (2026). https://pith.science/paper/NLKOL45S

@misc{pith2026260728921,
  author       = {Pith},
  title        = {Pith review of: Information Aggregation and Social Networks: Responsiveness and Overturning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NLKOL45S}},
  note         = {Machine review of arXiv:2607.28921}
}
read the original abstract

This paper studies how network structures affect the efficiency of information aggregation in social learning environments. We consider a model in which rational agents sequentially choose actions based on private signals and observations of their neighbors' actions in a network. Focusing on comparisons of expected payoffs at a given finite period, we show that there exists an information structure under which the star network achieves a strictly higher expected payoff than any other network, and another information structure under which the complete network achieves a strictly higher expected payoff than any other network. Taken together, these results imply that no network is uniformly optimal across all information structures. Our analysis highlights a trade-off between the responsiveness effect and the overturning effect: disconnected networks preserve responsiveness of actions to private signals, whereas highly connected networks facilitate the aggregation of extreme information that overturns public beliefs.

Figures

Figures reproduced from arXiv: 2607.28921 by the authors.

Figure 1
Figure 1. Networks in which agent 3 has no connection. The second category consists of networks in which agent 3 observes exactly one predecessor, and the observed predecessor’s action is not affected by any earlier action. These networks are shown in [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Networks in which agent 3 observes exactly one predecessor whose action is based only on her own private signal. The third category consists of the network in which agent 3 observes only agent 2’s action, while agent 2 observes agent 1’s action. This network is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Network in which agent 3 observes exactly one predecessor whose action may depend on another predecessor’s action. The fourth category consists of the network in which agent 3 observes both prede￾cessors, while agent 2 does not observe agent 1. This network is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Star network: agent 3 observes both predecessors, and agent 2 has no con [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Complete network: each agent observes all predecessors. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Star and complete networks Definition 1. A network 𝒩 is called a star network, denoted by 𝒩 𝑆 , if it satisfies 𝒩𝑖 = ∅ for 𝑖 = 1, 2, . . . , 𝑁 − 1 and 𝒩𝑁 = {1, 2, . . . , 𝑁 − 1}. A star network is the most dispersed network in the sense that no agent observes the actio…
Figure 7
Figure 7. Figure 7: Regions where the star and complete networks outperform each other [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Private-belief densities used in the numerical exercises [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Comparison of the complete network and the star network [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

114 extracted references · 5 linked inside Pith

  1. [1]

    The Annals of Mathematical Statistics , pages=

    Equivalent comparisons of experiments , author=. The Annals of Mathematical Statistics , pages=. 1953 , publisher=

    1953

  2. [2]

    American Economic Review , volume=

    Bayesian persuasion , author=. American Economic Review , volume=

  3. [3]

    Annual Review of Economics , volume=

    Bayesian persuasion and information design , author=. Annual Review of Economics , volume=. 2019 , publisher=

    2019

  4. [4]

    Journal of Economic Literature , volume=

    Information design: A unified perspective , author=. Journal of Economic Literature , volume=. 2019 , publisher=

    2019

  5. [5]

    Theoretical Economics , volume=

    Bayes correlated equilibrium and the comparison of information structures in games , author=. Theoretical Economics , volume=. 2016 , publisher=

    2016

  6. [6]

    American Economic Journal: Microeconomics , volume=

    Information design , author=. American Economic Journal: Microeconomics , volume=. 2019 , publisher=

    2019

  7. [7]

    American Economic Review , volume=

    Advertising content , author=. American Economic Review , volume=. 2006 , publisher=

    2006

  8. [8]

    Journal of Economic Theory , pages=

    Information design for selling search goods and the effect of competition , author=. Journal of Economic Theory , pages=. 2023 , publisher=

    2023

Show all 114 references
  1. [9]

    arXiv preprint arXiv:2303.13409 , year=

    Persuaded search , author=. arXiv preprint arXiv:2303.13409 , year=

    arXiv

  2. [10]

    1995 , publisher=

    Repeated games with incomplete information , author=. 1995 , publisher=

    1995

  3. [11]

    Working paper , year=

    Guided search , author=. Working paper , year=

  4. [12]

    American Economic Review: Insights , volume=

    Herd Design , author=. American Economic Review: Insights , volume=. 2023 , publisher=

    2023

  5. [13]

    Available at SSRN 4342503 , year=

    Information Design of Sponsored Advertising , author=. Available at SSRN 4342503 , year=

  6. [14]

    Economics Letters , volume=

    A model of Bayesian persuasion with transfers , author=. Economics Letters , volume=. 2017 , publisher=

    2017

  7. [15]

    Web and Internet Economics: 15th International Conference, WINE 2019, New York, NY, USA, December 10--12, 2019, Proceedings 15 , pages=

    Persuasion and incentives through the lens of duality , author=. Web and Internet Economics: 15th International Conference, WINE 2019, New York, NY, USA, December 10--12, 2019, Proceedings 15 , pages=. 2019 , organization=

    2019

  8. [16]

    Theoretical Economics , volume=

    Paying with information , author=. Theoretical Economics , volume=. 2023 , publisher=

    2023

  9. [17]

    Available at SSRN 4762231 , year=

    Designing Contracts and Information Jointly , author=. Available at SSRN 4762231 , year=

  10. [18]

    2022 , institution=

    Comparisons of signals , author=. 2022 , institution=

    2022

  11. [19]

    Journal of Economic Theory , volume=

    When are signals complements or substitutes? , author=. Journal of Economic Theory , volume=. 2013 , publisher=

    2013

  12. [20]

    Proceedings of the second Berkeley symposium on mathematical statistics and probability , volume=

    Comparison of experiments , author=. Proceedings of the second Berkeley symposium on mathematical statistics and probability , volume=. 1951 , organization=

    1951

  13. [21]

    Research in Economics , volume=

    The value of information in monotone decision problems , author=. Research in Economics , volume=. 2018 , publisher=

    2018

  14. [22]

    2011 , publisher=

    Comparing location experiments , booktitle=. 2011 , publisher=

    2011

  15. [23]

    Econometrica , volume=

    Information acquisition in auctions , author=. Econometrica , volume=. 2000 , publisher=

    2000

  16. [24]

    2018 , publisher=

    de Oliveira, Henrique , journal=. 2018 , publisher=

    2018

  17. [25]

    Annals of Statistics , volume=

    Comparing location experiments , author=. Annals of Statistics , volume=

  18. [26]

    Journal of Economic Theory , volume=

    On comparisons of information structures with infinite states , author=. Journal of Economic Theory , volume=. 2024 , publisher=

    2024

  19. [27]

    Whitmeyer, Mark , journal=. Bayes=

  20. [28]

    A geometric

    Wu, Wenhao , journal=. A geometric. 2023 , publisher=

    2023

  21. [29]

    2021 , institution=

    Coarse bayesian updating , author=. 2021 , institution=

    2021

  22. [30]

    Journal of Political Economy , volume=

    Non-bayesian persuasion , author=. Journal of Political Economy , volume=. 2022 , publisher=

    2022

  23. [31]

    Available at SSRN 4467608 , year=

    Privacy Preserving Signals , author=. Available at SSRN 4467608 , year=

  24. [32]

    Econometrica , volume=

    Extreme points and majorization: Economic applications , author=. Econometrica , volume=. 2021 , publisher=

    2021

  25. [33]

    AEA Papers and Proceedings , volume=

    Simplicity and probability weighting in choice under risk , author=. AEA Papers and Proceedings , volume=. 2022 , organization=

    2022

  26. [34]

    Available at SSRN 3253494 , year=

    Preference for simplicity , author=. Available at SSRN 3253494 , year=

  27. [35]

    Available at SSRN , volume=

    Simplicity and risk , author=. Available at SSRN , volume=

  28. [36]

    American Economic Review , volume=

    Quantifying information and uncertainty , author=. American Economic Review , volume=. 2019 , publisher=

    2019

  29. [37]

    Econometrica , volume=

    Pathological outcomes of observational learning , author=. Econometrica , volume=. 2000 , publisher=

    2000

  30. [38]

    The Quarterly Journal of Economics , volume=

    A simple model of herd behavior , author=. The Quarterly Journal of Economics , volume=. 1992 , publisher=

    1992

  31. [39]

    Journal of Political Economy , volume=

    A theory of fads, fashion, custom, and cultural change as informational cascades , author=. Journal of Political Economy , volume=. 1992 , publisher=

    1992

  32. [40]

    Econometrica , volume=

    Learning from reviews: The selection effect and the speed of learning , author=. Econometrica , volume=. 2022 , publisher=

    2022

  33. [41]

    IEEE Transactions on Signal and Information Processing over Networks , volume=

    Information cascades with noise , author=. IEEE Transactions on Signal and Information Processing over Networks , volume=. 2017 , publisher=

    2017

  34. [42]

    UB Economics--Working Papers, 2022, E22/434 , year=

    Persuading crowds , author=. UB Economics--Working Papers, 2022, E22/434 , year=

    2022

  35. [43]

    2021 , institution=

    Information cascades and social learning , author=. 2021 , institution=

    2021

  36. [44]

    Journal of Economic Theory , volume=

    Social learning with endogenous observation , author=. Journal of Economic Theory , volume=. 2016 , publisher=

    2016

  37. [45]

    Games and Economic Behavior , volume=

    Observational learning under imperfect information , author=. Games and Economic Behavior , volume=. 2004 , publisher=

    2004

  38. [46]

    American Economic Journal: Microeconomics , volume=

    Social learning with costly search , author=. American Economic Journal: Microeconomics , volume=. 2016 , publisher=

    2016

  39. [47]

    Available at SSRN 4498779 , year=

    Social Learning through Action-Signals , author=. Available at SSRN 4498779 , year=

  40. [48]

    Journal of Economic Theory , volume=

    Information design through scarcity and social learning , author=. Journal of Economic Theory , volume=. 2023 , publisher=

    2023

  41. [49]

    The Journal of finance , volume=

    Sequential sales, learning, and cascades , author=. The Journal of finance , volume=. 1992 , publisher=

    1992

  42. [50]

    The RAND Journal of Economics , volume=

    Dynamic monopoly pricing and herding , author=. The RAND Journal of Economics , volume=. 2006 , publisher=

    2006

  43. [51]

    Economic Theory , volume=

    Monopoly pricing in the binary herding model , author=. Economic Theory , volume=. 2008 , publisher=

    2008

  44. [52]

    Journal of Political Economy , volume=

    Search, information, and prices , author=. Journal of Political Economy , volume=. 2021 , publisher=

    2021

  45. [53]

    Games and Economic Behavior , volume=

    Optimizing information in the herd: Guinea pigs, profits, and welfare , author=. Games and Economic Behavior , volume=. 2002 , publisher=

    2002

  46. [54]

    The Review of Economic Studies , volume=

    Informational herding, optimal experimentation, and contrarianism , author=. The Review of Economic Studies , volume=. 2021 , publisher=

    2021

  47. [55]

    The Review of Economic Studies , volume=

    Bayesian learning in social networks , author=. The Review of Economic Studies , volume=. 2011 , publisher=

    2011

  48. [56]

    The Quarterly Journal of Economics , volume=

    Recommender systems as mechanisms for social learning , author=. The Quarterly Journal of Economics , volume=. 2018 , publisher=

    2018

  49. [57]

    Econometrica , volume=

    On the efficiency of social learning , author=. Econometrica , volume=. 2019 , publisher=

    2019

  50. [58]

    The Quarterly Journal of Economics , volume=

    Complementary information and learning traps , author=. The Quarterly Journal of Economics , volume=. 2020 , publisher=

    2020

  51. [59]

    Operations Research , volume=

    Bayesian social learning from consumer reviews , author=. Operations Research , volume=. 2019 , publisher=

    2019

  52. [60]

    Journal of Economic Theory , volume=

    Herding with costly information , author=. Journal of Economic Theory , volume=. 2018 , publisher=

    2018

  53. [61]

    American Economic Journal: Microeconomics , volume=

    Observational learning and demand for search goods , author=. American Economic Journal: Microeconomics , volume=. 2012 , publisher=

    2012

  54. [62]

    Econometrica , volume=

    Beyond unbounded beliefs: How preferences and information interplay in social learning , author=. Econometrica , volume=. 2024 , publisher=

    2024

  55. [63]

    Games and Economic Behavior , volume=

    Word-of-mouth learning , author=. Games and Economic Behavior , volume=. 2004 , publisher=

    2004

  56. [64]

    Journal of Economic Theory , volume=

    The wisdom of the minority , author=. Journal of Economic Theory , volume=. 2009 , publisher=

    2009

  57. [65]

    Games and Economic Behavior , volume=

    Bayesian learning in social networks , author=. Games and Economic Behavior , volume=. 2003 , publisher=

    2003

  58. [66]

    Available at SSRN 1138095 , year=

    Rational social learning by random sampling , author=. Available at SSRN 1138095 , year=

  59. [67]

    International Game Theory Review , volume=

    Herding with costly information , author=. International Game Theory Review , volume=. 2006 , publisher=

    2006

  60. [68]

    The BE Journal of Theoretical Economics , volume=

    Herding with costly observation , author=. The BE Journal of Theoretical Economics , volume=. 2007 , publisher=

    2007

  61. [69]

    The Review of Economic Studies , volume=

    Reputation building under observational learning , author=. The Review of Economic Studies , volume=. 2023 , publisher=

    2023

  62. [70]

    The Review of Economic Studies , volume=

    Multidimensional social learning , author=. The Review of Economic Studies , volume=. 2019 , publisher=

    2019

  63. [71]

    Mathematics of Operations Research , volume=

    A general analysis of sequential social learning , author=. Mathematics of Operations Research , volume=. 2021 , publisher=

    2021

  64. [72]

    Theoretical Economics , volume=

    Information diffusion in networks through social learning , author=. Theoretical Economics , volume=. 2015 , publisher=

    2015

  65. [73]

    Journal of Economic Theory , volume=

    A monopolistic market for information , author=. Journal of Economic Theory , volume=. 1986 , publisher=

    1986

  66. [74]

    The American Economic Review , volume=

    Selling and trading on information in financial markets , author=. The American Economic Review , volume=. 1988 , publisher=

    1988

  67. [75]

    Econometrica: Journal of the Econometric Society , pages=

    Direct and indirect sale of information , author=. Econometrica: Journal of the Econometric Society , pages=. 1990 , publisher=

    1990

  68. [76]

    The Rand Journal of Economics , volume=

    The price of advice , author=. The Rand Journal of Economics , volume=. 2007 , publisher=

    2007

  69. [77]

    American Economic Journal: Microeconomics , volume=

    Selling cookies , author=. American Economic Journal: Microeconomics , volume=. 2015 , publisher=

    2015

  70. [78]

    American economic review , volume=

    The design and price of information , author=. American economic review , volume=. 2018 , publisher=

    2018

  71. [79]

    Annual Review of Economics , volume=

    Markets for information: An introduction , author=. Annual Review of Economics , volume=. 2019 , publisher=

    2019

  72. [80]

    arXiv preprint arXiv:2408.17398 , year=

    Robust Technology Regulation , author=. arXiv preprint arXiv:2408.17398 , year=

  73. [81]

    Journal of Economic theory , volume=

    On the convergence of informational cascades , author=. Journal of Economic theory , volume=. 1993 , publisher=

    1993

  74. [82]

    Journal of Economic Literature , volume=

    Information cascades and social learning , author=. Journal of Economic Literature , volume=. 2024 , publisher=

    2024

  75. [83]

    Econometrica: Journal of the Econometric Society , pages=

    Monotone comparative statics , author=. Econometrica: Journal of the Econometric Society , pages=. 1994 , publisher=

    1994

  76. [84]

    The Pisitive Effect of Garbling on Social Learning , author=

  77. [85]

    Mu, Xiaosheng and Pomatto, Luciano and Strack, Philipp and Tamuz, Omer , journal=. From. 2021 , publisher=

    2021

  78. [86]

    American Economic Review , volume=

    Comparisons of signals , author=. American Economic Review , volume=. 2024 , publisher=

    2024

  79. [87]

    Econometrica , volume=

    The law of large demand for information , author=. Econometrica , volume=. 2002 , publisher=

    2002

  80. [88]

    Available at SSRN 2722234 , year=

    Strategically valuable information , author=. Available at SSRN 2722234 , year=

  81. [89]

    Games and Economic Behavior , volume=

    Comparison of information structures , author=. Games and Economic Behavior , volume=. 2000 , publisher=

    2000

  82. [90]

    Games and Economic Behavior , volume=

    Signaling and mediation in games with common interests , author=. Games and Economic Behavior , volume=. 2010 , publisher=

    2010

  83. [91]

    Games and Economic Behavior , volume=

    Garbling of signals and outcome equivalence , author=. Games and Economic Behavior , volume=. 2013 , publisher=

    2013

  84. [92]

    Games and Economic Behavior , volume=

    Comparison of information structures in zero-sum games , author=. Games and Economic Behavior , volume=. 2008 , publisher=

    2008

  85. [93]

    the law of large demand for information

    Comment on “the law of large demand for information” , author=. Econometrica , volume=. 2014 , publisher=

    2014

  86. [94]

    New characterization of

    Ben-Shahar, Danny and Sulganik, Eyal , journal=. New characterization of. 2024 , publisher=

    2024

  87. [95]

    University of Chicago , year=

    Notes on the comparison of experiments , author=. University of Chicago , year=

  88. [96]

    arXiv preprint arXiv:2405.16458 , year=

    Comparing experiments in discounted problems , author=. arXiv preprint arXiv:2405.16458 , year=

    arXiv

  89. [97]

    arXiv preprint arXiv:2407.16648 , year=

    Dynamic Signals , author=. arXiv preprint arXiv:2407.16648 , year=

    arXiv

  90. [98]

    1991 , publisher=

    Comparison of statistical experiments , author=. 1991 , publisher=

    1991

  91. [99]

    Zeitschrift f

    Comparison of experiments when the parameter space is finite , author=. Zeitschrift f. 1970 , publisher=

    1970

  92. [100]

    arXiv preprint arXiv:2406.05299 , year=

    Learning about informativeness , author=. arXiv preprint arXiv:2406.05299 , year=

    arXiv

  93. [101]

    Journal of Economic Theory , volume=

    The speed of sequential asymptotic learning , author=. Journal of Economic Theory , volume=. 2018 , publisher=

    2018

  94. [102]

    Available at SSRN 5147454 , year=

    Social Learning with Markovian Information , author=. Available at SSRN 5147454 , year=

  95. [103]

    The Annals of Statistics , volume=

    Comparison of sequential experiments , author=. The Annals of Statistics , volume=. 1996 , publisher=

    1996

  96. [104]

    arXiv preprint arXiv:2405.13709 , year=

    Comparisons of sequential experiments for additively separable problems , author=. arXiv preprint arXiv:2405.13709 , year=

    arXiv

  97. [105]

    Journal of Economic Theory , pages=

    Social learning through coarse signals of others' actions , author=. Journal of Economic Theory , pages=. 2025 , publisher=

    2025

  98. [106]

    Actualites Scientifiques et Industrielles , volume=

    Sur un nouveau theoreme-limite de la theorie des probabilites , author=. Actualites Scientifiques et Industrielles , volume=

  99. [107]

    Journal of Political Economy , volume=

    Learning efficiency of multiagent information structures , author=. Journal of Political Economy , volume=. 2023 , publisher=

    2023

  100. [108]

    Learning in social networks

    Golub, Benjamin and Sadler, Evan , isbn =. Learning in social networks. The Oxford Handbook of the Economics of Networks. 2016 , month =

    2016

  101. [109]

    Econometrica , volume=

    Strategic learning and the topology of social networks , author=. Econometrica , volume=. 2015 , publisher=

    2015

  102. [110]

    arXiv preprint arXiv:1911.10116 , year=

    Aggregative efficiency of bayesian learning in networks , author=. arXiv preprint arXiv:1911.10116 , year=

    1911

  103. [111]

    Economics Letters , volume=

    On the role of responsiveness in rational herds , author=. Economics Letters , volume=. 2018 , publisher=

    2018

  104. [112]

    American Economic Journal: Microeconomics , volume=

    Naive learning in social networks and the wisdom of crowds , author=. American Economic Journal: Microeconomics , volume=. 2010 , publisher=

    2010

  105. [113]

    Review of Economic Studies , volume=

    Learning from neighbours about a changing state , author=. Review of Economic Studies , volume=. 2023 , publisher=

    2023

  106. [114]

    The Quarterly Journal of Economics , volume=

    Extensive imitation is irrational and harmful , author=. The Quarterly Journal of Economics , volume=. 2014 , publisher=

    2014

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.