IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v213y2023ics0022053123001291.html
   My bibliography  Save this article

Linear Riley equilibria in quadratic signaling games

Author

Listed:
  • Weng, Xi
  • Wu, Fan
  • Yin, Xundong

Abstract

We study signaling games with quadratic payoffs. As signaling games admit multiple separating equilibria, many equilibrium selection rules are proposed and a well-known solution is Riley equilibria. They are separating equilibria in which the sender achieves the highest equilibrium payoff for all types among all separating equilibria. We analyze the conditions for Riley equilibria to be linear, a common assumption in many applications. We derive a sufficient and necessary condition for the existence and uniqueness of linear Riley equilibria. We apply the result to confirm the dominance of linear equilibria in some classic examples, and we show that, in some other examples, there exist previously unknown nonlinear Riley equilibria.

Suggested Citation

  • Weng, Xi & Wu, Fan & Yin, Xundong, 2023. "Linear Riley equilibria in quadratic signaling games," Journal of Economic Theory, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:jetheo:v:213:y:2023:i:c:s0022053123001291
    DOI: 10.1016/j.jet.2023.105733
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053123001291
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2023.105733?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Milgrom, Paul & Roberts, John, 1982. "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica, Econometric Society, vol. 50(2), pages 443-459, March.
    2. Ramey, Garey, 1996. "D1 Signaling Equilibria with Multiple Signals and a Continuum of Types," Journal of Economic Theory, Elsevier, vol. 69(2), pages 508-531, May.
    3. Navin Kartik, 2009. "Strategic Communication with Lying Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1359-1395.
    4. Philippe Aghion & Mathias Dewatripont & Patrick Rey, 2004. "Transferable Control," Journal of the European Economic Association, MIT Press, vol. 2(1), pages 115-138, March.
    5. Hermalin, Benjamin E, 1998. "Toward an Economic Theory of Leadership: Leading by Example," American Economic Review, American Economic Association, vol. 88(5), pages 1188-1206, December.
    6. Riley, John G, 1979. "Informational Equilibrium," Econometrica, Econometric Society, vol. 47(2), pages 331-359, March.
    7. Wouter Dessein, 2002. "Authority and Communication in Organizations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 811-838.
    8. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 79-130, May.
    9. Mailath, George J. & von Thadden, Ernst-Ludwig, 2013. "Incentive compatibility and differentiability: New results and classic applications," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1841-1861.
    10. Mailath, George J, 1987. "Incentive Compatibility in Signaling Games with a Continuum of Types," Econometrica, Econometric Society, vol. 55(6), pages 1349-1365, November.
    11. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    12. Riley, John G., 1975. "Competitive signalling," Journal of Economic Theory, Elsevier, vol. 10(2), pages 174-186, April.
    13. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    14. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    15. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    16. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    17. Kartik, Navin & Ottaviani, Marco & Squintani, Francesco, 2007. "Credulity, lies, and costly talk," Journal of Economic Theory, Elsevier, vol. 134(1), pages 93-116, May.
    18. Noldeke, Georg & Samuelson, Larry, 1997. "A Dynamic Model of Equilibrium Selection in Signaling Markets," Journal of Economic Theory, Elsevier, vol. 73(1), pages 118-156, March.
    19. Cho, In-Koo & Sobel, Joel, 1990. "Strategic stability and uniqueness in signaling games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 381-413, April.
    20. Philippe Aghion & Mathias Dewatripont & Patrick Rey, 2004. "Transferable Control," Journal of the European Economic Association, MIT Press, vol. 2(1), pages 115-138, March.
    21. Zhou, Junjie, 2016. "Economics of leadership and hierarchy," Games and Economic Behavior, Elsevier, vol. 95(C), pages 88-106.
    22. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    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. Hedlund, Jonas, 2017. "Bayesian persuasion by a privately informed sender," Journal of Economic Theory, Elsevier, vol. 167(C), pages 229-268.
    2. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    3. Han, Seungjin & Sam, Alex & Shin, Youngki, 2024. "Monotone equilibrium in matching markets with signaling," Journal of Economic Theory, Elsevier, vol. 216(C).
    4. Peter Eso & James Schummer, 2005. "Robust Deviations from Signaling Equilibria," Discussion Papers 1406, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Navin Kartik, 2009. "Strategic Communication with Lying Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1359-1395.
    6. Manelli, Alejandro M., 1997. "The Never-a-Weak-Best-Response Test in Infinite Signaling Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 152-173, May.
    7. Etro, Federico, 2017. "Research in economics and game theory. A 70th anniversary," Research in Economics, Elsevier, vol. 71(1), pages 1-7.
    8. Andrew T Little, 2023. "Bayesian explanations for persuasion," Journal of Theoretical Politics, , vol. 35(3), pages 147-181, July.
    9. Vaccari, Federico, 2023. "Competition in costly talk," Journal of Economic Theory, Elsevier, vol. 213(C).
    10. Noldeka, G. & Samuelson, L., 1994. "Learning to Signal in Market," Working papers 9409, Wisconsin Madison - Social Systems.
    11. James W. Roberts & Andrew Sweeting, 2013. "When Should Sellers Use Auctions?," American Economic Review, American Economic Association, vol. 103(5), pages 1830-1861, August.
    12. Little, Andrew T., 2022. "Bayesian Explanations for Persuasion," OSF Preprints ygw8e, Center for Open Science.
    13. Noldeke, Georg & Samuelson, Larry, 1997. "A Dynamic Model of Equilibrium Selection in Signaling Markets," Journal of Economic Theory, Elsevier, vol. 73(1), pages 118-156, March.
    14. Christopher Gedge & James W. Roberts & Andrew Sweeting, 2014. "A Model of Dynamic Limit Pricing with an Application to the Airline Industry," NBER Working Papers 20293, National Bureau of Economic Research, Inc.
    15. Kübler, Dorothea & Müller, Wieland & Normann, Hans-Theo, 2008. "Job-market signaling and screening: An experimental comparison," Games and Economic Behavior, Elsevier, vol. 64(1), pages 219-236, September.
    16. Axel Gautier & Dimitri Paolini, 2007. "Delegation and Information Revelation," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 163(4), pages 574-597, December.
    17. Vaccari, Federico, 2021. "Competition in Signaling," MPRA Paper 106071, University Library of Munich, Germany.
    18. Dosis, Anastasios, 2018. "On signalling and screening in markets with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 140-149.
    19. Johanna Hertel & John Smith, 2013. "Not so cheap talk: costly and discrete communication," Theory and Decision, Springer, vol. 75(2), pages 267-291, August.
    20. Péter Eső & James Schummer, 2009. "Credible deviations from signaling equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 411-430, November.

    More about this item

    Keywords

    Signaling; Riley equilibria; Linear strategy;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:eee:jetheo:v:213:y:2023:i:c:s0022053123001291. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.