IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/655.html

Effects of Noise on the Grammar of Languages

Author

Listed:
  • Bauch, Gerrit

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We study a signaling game of common interest in which a stochastic noise is perturbing the communication between an informed sender and an uninformed receiver. Despite this inhibiting factor, efficient languages exist. In equilibrium, sender uses a tessellation consisting of convex cells while receiver converts posterior beliefs into Bayesian estimators serving as interpretations. Shannon entropy measures the noise level and describes to which extent communication is possible. A limit case of errors that respect the distance between words leads to concise interpretations in the decoding process. Comparative statics for different levels of noise reveal which grammatical structures are more robust towards noise. For increasing error separation between most distinct types becomes more important than precision about each single one. Furthermore, distinct words are saved for the description of opposite domains of the type space. Evolutionary modeling approaches converge to equilibria, but not every equilibrium is stable.

Suggested Citation

  • Bauch, Gerrit, 2021. "Effects of Noise on the Grammar of Languages," Center for Mathematical Economics Working Papers 655, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:655
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2957927/2957930
    File Function: First Version, 2021
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Besley, Timothy & Smart, Michael, 2007. "Fiscal restraints and voter welfare," Journal of Public Economics, Elsevier, vol. 91(3-4), pages 755-773, April.
    2. Jäger, Gerhard & Koch-Metzger, Lars & Riedel, Frank, 2011. "Voronoi languages. Equilibria in cheap-talk games with high-dimensional types and few signals," Center for Mathematical Economics Working Papers 420, Center for Mathematical Economics, Bielefeld University.
    3. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    4. Andreas Blume, 2004. "A Learning-Efficiency Explanation of Structure in Language," Theory and Decision, Springer, vol. 57(3), pages 265-285, November.
    5. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
    6. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blume, Andreas & Noussair, Charles N. & Ye, Bohan, 2024. "Fragile meaning - an experiment," Journal of Economic Theory, Elsevier, vol. 216(C).
    2. Penélope Hernández & Bernhard von Stengel, 2014. "Nash Codes for Noisy Channels," Operations Research, INFORMS, vol. 62(6), pages 1221-1235, December.
    3. Nasimeh Heydaribeni & Achilleas Anastasopoulos, 2019. "Linear Equilibria for Dynamic LQG Games with Asymmetric Information and Dependent Types," Papers 1909.04834, arXiv.org.
    4. Aleksei Smirnov & Egor Starkov, 2019. "Timing of predictions in dynamic cheap talk: experts vs. quacks," ECON - Working Papers 334, Department of Economics - University of Zurich.
    5. Suehyun Kwon, 2018. "Selling Complementary Goods: Information and Products," CESifo Working Paper Series 7394, CESifo.
    6. Hagenbach, Jeanne & Koessler, Frédéric, 2020. "Cheap talk with coarse understanding," Games and Economic Behavior, Elsevier, vol. 124(C), pages 105-121.
    7. Dilmé, Francesc, 2023. "Communication between unbiased agents," Games and Economic Behavior, Elsevier, vol. 142(C), pages 613-622.
    8. Redlicki, Bartosz & Redlicki, Jakub, 2022. "Communication with Costly and Detectable Falsification," Journal of Economic Behavior & Organization, Elsevier, vol. 202(C), pages 452-470.
    9. Au, Pak Hung & Kawai, Keiichi, 2020. "Competitive information disclosure by multiple senders," Games and Economic Behavior, Elsevier, vol. 119(C), pages 56-78.
    10. Blume, Andreas, 2018. "Failure of common knowledge of language in common-interest communication games," Games and Economic Behavior, Elsevier, vol. 109(C), pages 132-155.
    11. Johanna Hertel & John Smith, 2013. "Not so cheap talk: costly and discrete communication," Theory and Decision, Springer, vol. 75(2), pages 267-291, August.
    12. Ayouni, Mehdi & Friehe, Tim & Gabuthy, Yannick, 2024. "Bayesian persuasion in lawyer–client communication," International Review of Law and Economics, Elsevier, vol. 78(C).
    13. Caldieraro, Fabio & Cunha, Marcus, 2022. "Consumers’ response to weak unique selling propositions: Implications for optimal product recommendation strategy," International Journal of Research in Marketing, Elsevier, vol. 39(3), pages 724-744.
    14. Boris Knapp, 2021. "Fake Reviews and Naive Consumers," Vienna Economics Papers 2102, University of Vienna, Department of Economics.
    15. Szalay, Dezső & Deimen, Inga, 2015. "Information, authority, and smooth communication in organizations," CEPR Discussion Papers 10969, C.E.P.R. Discussion Papers.
    16. Toru Suzuki, 2021. "Pragmatic Ambiguity and Rational Miscommunication," Working Paper Series 2021/04, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    17. Jeanne Hagenbach & Frédéric Koessler, 2019. "Partial Language Competence," Working Papers hal-03393108, HAL.
    18. Antony Millner & Hélène Ollivier, 2016. "Beliefs, Politics, and Environmental Policy," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 10(2), pages 226-244.
    19. Isaiah Andrews & Jesse M. Shapiro, 2021. "A Model of Scientific Communication," Econometrica, Econometric Society, vol. 89(5), pages 2117-2142, September.
    20. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:655. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.