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arxiv: 2605.28985 · v1 · pith:VLJOZGSWnew · submitted 2026-05-27 · 💰 econ.TH

Subsidizing Sequential Search

Salvador Candelas , Nicole Immorlica , Brendan Lucier This is my paper

Pith reviewed 2026-06-29 08:55 UTC · model grok-4.3

classification 💰 econ.TH
keywords sequential searchsubsidiesconsumer inspectionequilibrium refinementinformation revelationplatform pricingsearch order
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The pith

Higher-quality firms offer larger subsidies for consumer inspection, leading to search in descending subsidy order.

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

The paper examines markets where firms compete for attention by subsidizing the cost of inspecting their products. It establishes a subsidy-sorting principle under which higher-quality firms give weakly larger subsidies in any equilibrium, so consumers inspect in descending subsidy order. A unique equilibrium selected by forward-induction reasoning has low-quality firms never inspected, intermediate-quality firms separating with strictly increasing subsidies, and high-quality firms pooling at the full subsidy. This outcome maximizes information revelation and produces efficient inspection. The analysis extends to platforms selling inspection tokens, where linear pricing induces excessive inspection that reallocates surplus without lowering consumer welfare.

Core claim

In markets where firms subsidize the cost of product inspection to attract consumer attention, the subsidy-sorting principle holds: higher-quality firms give weakly larger subsidies in any equilibrium. Consumers therefore search in descending order of subsidies. The unique equilibrium that survives the Intuitive Criterion refinement has low-quality firms never inspected, intermediate-quality firms separating via strictly increasing subsidies, and high-quality firms pooling at the maximum subsidy level. This equilibrium maximizes information revelation and achieves efficient inspection. On AI platforms that price inspection tokens linearly, the optimum induces more inspection than socially op

What carries the argument

The subsidy-sorting principle, which links higher firm quality to weakly larger subsidies and thereby determines the consumer search order.

Load-bearing premise

Firms and consumers share common knowledge of the quality distribution and refine equilibria according to the Intuitive Criterion.

What would settle it

An observation that consumers inspect a low-quality firm while higher-quality firms offer equal or smaller subsidies would contradict the subsidy-sorting principle.

Figures

Figures reproduced from arXiv: 2605.28985 by Brendan Lucier, Nicole Immorlica, Salvador Candelas.

Figure 1
Figure 1. Figure 1: Low types are never inspected, intermediate types separate with strictly increasing subsidies, and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The shaded regions mark subsidy levels that make trade infeasible. In red, inspection yields negative [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Optimal separating subsidies. Parameters: Fpxq “ x, c “ 0.5, n “ 10. Panel (a): p “ 1.8. Panel (b): p “ 1. is inspected only after free inspection firms are exhausted. On the other hand, congestion dilutes attention: as more types join the pool, tie–breaking reduce each firm’s inspection probability. Let q poolpxq P p0, 1s denote the inspection probability of a firm offering the full subsidy s “ c when all… view at source ↗
Figure 4
Figure 4. Figure 4: Example of a SIS subsidy policy Definition 5 (Step–increasing–step family). For any t0 P rt, maxtcp, 1us, define the subsidy policy σ ˚ p¨ ; t0q : T Ñ r0, cs by σ ˚ pt; tq “ $ ’’’’’’& ’’’’’’% 0, t ă t0, t p ´ şt t0 q sep n px; t0q dx p q sep n pt; t0q , t P rt0, t1s, c, t ą t1, where qsep n p¨ ; t0q denotes the inspection probability under separation with boundary t0, and t1 is the unique solution to pt1 ´… view at source ↗
read the original abstract

We study markets where firms compete for consumer attention by subsidizing costly product inspection. These subsidies do not change product quality, but they alter the order in which consumers search by lowering inspection costs. We establish a subsidy-sorting principle: in any equilibrium, higher-quality firms provide weakly larger subsidies, leading consumers to search in descending subsidy order. A unique equilibrium survives forward-induction reasoning in the spirit of the Intuitive Criterion: low-quality firms are never inspected, intermediate-quality firms separate with strictly increasing subsidies, and high-quality firms pool at the full subsidy. This equilibrium maximizes information revelation among all possible outcomes and ensures efficient inspection. We then extend the analysis to AI-mediated platforms that can create and price inspection tokens. The platform's optimal linear pricing leads to excessive inspection relative to the social optimum. While this distortion does not reduce consumer welfare, it reallocates surplus from sellers to the platform and consumers.

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 manuscript analyzes markets in which firms compete for consumer attention by offering subsidies that reduce the cost of product inspection. It establishes a subsidy-sorting principle that holds in any equilibrium: higher-quality firms provide weakly larger subsidies, inducing consumers to search in descending order of subsidies. A unique equilibrium is selected by forward-induction reasoning in the spirit of the Intuitive Criterion, in which low-quality firms are never inspected, intermediate-quality firms separate with strictly increasing subsidies, and high-quality firms pool at the full subsidy. This equilibrium maximizes information revelation and ensures efficient inspection. The analysis is extended to AI-mediated platforms that create and price inspection tokens, where the platform's optimal linear pricing results in excessive inspection relative to the social optimum without reducing consumer welfare, but reallocating surplus from sellers to the platform and consumers.

Significance. The subsidy-sorting principle and the characterization of the unique equilibrium under the Intuitive Criterion represent a novel contribution to the theory of sequential search with endogenous inspection costs. The result that the equilibrium is informationally efficient is noteworthy. The extension to platform pricing provides a clear welfare analysis showing no consumer harm despite distortion. These findings could influence models of attention markets and platform regulation if the derivations are robust.

minor comments (2)
  1. The abstract and introduction should explicitly state the precise definition of the Intuitive Criterion refinement employed and how it differs from standard applications in signaling games, to allow readers to verify the uniqueness claim.
  2. In the platform extension, the statement that excessive inspection 'does not reduce consumer welfare' requires an explicit comparison of consumer surplus under platform pricing versus the social optimum; this calculation should be highlighted in the main text or appendix.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the thorough and positive assessment of our manuscript. The recommendation for minor revision is noted, and we are pleased that the subsidy-sorting principle, equilibrium selection via forward induction, informational efficiency, and platform extension were viewed as novel contributions.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from primitives

full rationale

The paper derives a subsidy-sorting principle and equilibrium selection via the Intuitive Criterion directly from standard sequential-search game primitives (common-knowledge quality distribution, inspection costs, forward-induction refinement). No fitted parameters are relabeled as predictions, no self-citations supply load-bearing uniqueness theorems, and no ansatz or renaming reduces the central claims to inputs by construction. The equilibrium configuration (low-quality firms uninspected, intermediate separation, high-quality pooling) follows from the refinement applied to the strategy space; the platform extension likewise follows from the same primitives without internal reduction. This is the normal case of a self-contained theoretical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The model rests on standard assumptions of rational Bayesian consumers, common knowledge of the quality distribution, and the Intuitive Criterion refinement; no free parameters or invented entities are introduced in the abstract.

axioms (3)
  • domain assumption Consumers are rational Bayesian updaters who choose search order and stopping rules to maximize expected utility net of inspection costs.
    Invoked to derive the subsidy-sorting principle and equilibrium inspection behavior.
  • domain assumption Firms simultaneously choose subsidies knowing that consumers will search in subsidy order.
    Required for the equilibrium concept and sorting result.
  • domain assumption The Intuitive Criterion (forward-induction refinement) selects among multiple equilibria.
    Used to obtain uniqueness and the specific low/intermediate/high quality partition.

pith-pipeline@v0.9.1-grok · 5673 in / 1549 out tokens · 21428 ms · 2026-06-29T08:55:40.679888+00:00 · methodology

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Reference graph

Works this paper leans on

22 extracted references · 11 canonical work pages

  1. [1]

    Advertising Content.American Economic Review96, 1 (March 2006), 93–113.https://doi.org/10.1257/000282806776157632 Susan Athey and Glenn Ellison

    work page doi:10.1257/000282806776157632 2006

  2. [2]

    Position Auctions with Consumer Search.The Quarterly Journal of Economics126, 3 (2011), 1213–1270.https://doi.org/10.1093/qje/qjr028 Pak Hung Au and Mark Whitmeyer

    work page doi:10.1093/qje/qjr028 2011

  3. [3]

    Attraction versus Persuasion: Information Provision in Search Markets.Journal of Political Economy131, 1 (2023), 202–245.https://doi.org/10.1086/ 720984 Jeffrey S Banks and Joel Sobel

    2023

  4. [4]

    Simon Board and Jay Lu

    Equilibrium selection in signaling games.Econometrica55, 3 (1987), 647–661. Simon Board and Jay Lu

    1987

  5. [5]

    1965–2010.https://www.jstor.org/stable/26550518 Hector Chade and Lones Smith

    Competitive Information Disclosure in Search Markets.Journal of Political Economy126, 5 (2018), pp. 1965–2010.https://www.jstor.org/stable/26550518 Hector Chade and Lones Smith

    work page arXiv 2018

  6. [6]

    Yongmin Chen and Chuan He

    Simultaneous search.Econometrica74, 5 (2006), 1293–1307. Yongmin Chen and Chuan He

    2006

  7. [7]

    In-Koo Cho and David M Kreps

    Paid Placement: Advertising and Search on the Internet.The Economic Journal121, 556 (2011), F309–F328. In-Koo Cho and David M Kreps

    2011

  8. [8]

    Peter A Diamond

    Signaling Games and Stable Equilibria.The Quarterly Journal of Economics102, 2 (1987), 179–221. Peter A Diamond

    1987

  9. [9]

    https://doi.org/10.1016/0022-0531(71)90013-5 Bolin Ding, Yiding Feng, Chien-Ju Ho, Wei Tang, and Haifeng Xu

    A model of price adjustment.Journal of Economic Theory3 (1971), 156–168. https://doi.org/10.1016/0022-0531(71)90013-5 Bolin Ding, Yiding Feng, Chien-Ju Ho, Wei Tang, and Haifeng Xu

    work page doi:10.1016/0022-0531(71)90013-5 1971

  10. [10]

    arXiv:2103.03769 [cs.GT]https://arxiv.org/abs/2103.03769 Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz

    Competitive Information Design for Pandora’s Box. arXiv:2103.03769 [cs.GT]https://arxiv.org/abs/2103.03769 Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz

    work page arXiv

  11. [11]

    Internet Advertising and the 26 Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords.American Eco- nomic Review97, 1 (2007), 242–259.https://doi.org/10.1257/aer.97.1.242 Glenn Ellison and Alexander Wolitzky

    work page doi:10.1257/aer.97.1.242 2007

  12. [12]

    Maarten Janssen, Thomas Jungbauer, Marcel Preuss, and Cole Williams

    A search cost model of obfuscation.The RAND Journal of Economics43, 3 (2012), 417–441. Maarten Janssen, Thomas Jungbauer, Marcel Preuss, and Cole Williams

    2012

  13. [13]

    J J McCall

    Sequential equilibria.Econometrica(1982), 863–894. J J McCall

    1982

  14. [14]

    Teddy Mekonnen, Zeky Murra-Anton, and Bobak Pakzad-Hurson

    Economics of Information and Job Search.The Quarterly Journal of Economics84, 1 (1970), 113–126. Teddy Mekonnen, Zeky Murra-Anton, and Bobak Pakzad-Hurson

    1970

  15. [15]

    Persuaded Search.Journal of Political Economy133, 10 (2025), 3167–3207.https://doi.org/10.1086/736765 Paul Milgrom and Chris Shannon

    work page doi:10.1086/736765 2025

  16. [16]

    Monotone Comparative Statics.Econometrica62, 1 (1994), 157–180.https://doi.org/10.2307/2951479 Volker Nocke and Patrick Rey

    work page doi:10.2307/2951479 1994

  17. [17]

    Consumer Search, Steering, and Choice Overload.Journal of Political Economy132, 5 (May 2024), 1684–1739.https://doi.org/10.1086/728108 Jean-Charles Rochet and Jean Tirole

    work page doi:10.1086/728108 2024

  18. [18]

    Rothschild, Markus Mobius, Jake M

    Platform Competition in Two-Sided Markets.Jour- nal of the European Economic Association1, 4 (2003), 990–1029.https://doi.org/10.1162/ 154247603322493212 David M. Rothschild, Markus Mobius, Jake M. Hofman, Eleanor W. Dillon, Daniel G. Goldstein, Nicole Immorlica, Sonia Jaffe, Brendan Lucier, Aleksandrs Slivkins, and Matthew Vogel

    2003

  19. [19]

    arXiv:2505.15799 [cs.CY]https://arxiv.org/abs/2505.15799 George J

    The Agentic Economy. arXiv:2505.15799 [cs.CY]https://arxiv.org/abs/2505.15799 George J. Stigler

    work page arXiv

  20. [20]

    The Economics of Information.Journal of Political Economy69, 3 (1961), 213–

    1961

  21. [21]

    https://doi.org/10.2307/1910412 E Glen Weyl

    Optimal Search for the Best Alternative.Econometrica47, 3 (1979), 641–654. https://doi.org/10.2307/1910412 E Glen Weyl

    work page doi:10.2307/1910412 1979

  22. [22]

    27 A Omitted proofs for Section 3 A.1 Proof of Lemma 1 First, we establish that the attention function is weakly increasing on path

    A price theory of multi-sided platforms.American Economic Review100, 4 (2010), 1642–1672. 27 A Omitted proofs for Section 3 A.1 Proof of Lemma 1 First, we establish that the attention function is weakly increasing on path. Claim 1.For s,s 1 PImpσq, if s 1 ěs, then q σ,ιps1q ěq σ,ιpsq. Proof.Assume towards a contradiction that this is not the case, thenq σ...

    2010