IDEAS home Printed from https://ideas.repec.org/p/iek/wpaper/2204.html
   My bibliography  Save this paper

Grand Mechanism and Population Uncertainty

Author

Listed:
  • Bara Kim

    (Department of Mathematics, Korea University, South Korea)

  • Seung Han Yoo

    (Department of Economics, Korea University, South Korea)

Abstract

This paper studies an informed mechanism designer problem in which the principal's private information is a number of agents. The principal designs both a protocol structure with respect to how to reveal the information and a collection of sub-mechanisms. The former is a mapping from numbers of agents to probability distributions over information revelation rules, and the latter's different sub-mechanisms may each contain unique allocation and payment functions depending on the principal's private information as well as a rule. Since choosing a protocol structure and such a collection are interwoven, we establish the existence of the grand mechanism using an expected payoff linearity. Then, we show that there is a single threshold for the optimal grand mechanism if a sub-mechanism cannot depend on the principal's private information. Interestingly, the main result shows that if a sub-mechanism can also depend on his private information, the optimal grand mechanism is characterized by double thresholds such that the principal does not announce the number of agents if it is in the middle range. We further extend the protocol structure to include rich sets of rules.

Suggested Citation

  • Bara Kim & Seung Han Yoo, 2022. "Grand Mechanism and Population Uncertainty," Discussion Paper Series 2204, Institute of Economic Research, Korea University.
    • Handle: RePEc:iek:wpaper:2204
    as

    Download full text from publisher

    File URL: http://econ.korea.ac.kr/~ri/WorkingPapers/w2204.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-1797, November.
    2. Jingfeng Lu, 2009. "Auction design with opportunity cost," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 73-103, January.
    3. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Frédéric Koessler & Vasiliki Skreta, 2023. "Informed Information Design," Journal of Political Economy, University of Chicago Press, vol. 131(11), pages 3186-3232.
    7. Paulo K. Monteiro & Flavio M. Menezes, 2000. "original papers : Auctions with endogenous participation," Review of Economic Design, Springer;Society for Economic Design, vol. 5(1), pages 71-89.
    8. Maskin, Eric & Tirole, Jean, 1992. "The Principal-Agent Relationship with an Informed Principal, II: Common Values," Econometrica, Econometric Society, vol. 60(1), pages 1-42, January.
    9. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    10. Jullien, B. & Mariotti, T., 2006. "Auction and the informed seller problem," Games and Economic Behavior, Elsevier, vol. 56(2), pages 225-258, August.
    11. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    12. Levin, Dan & Ozdenoren, Emre, 2004. "Auctions with uncertain numbers of bidders," Journal of Economic Theory, Elsevier, vol. 118(2), pages 229-251, October.
    13. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    14. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    15. Maskin, Eric & Tirole, Jean, 1990. "The Principal-Agent Relationship with an Informed Principal: The Case of Private Values," Econometrica, Econometric Society, vol. 58(2), pages 379-409, March.
    16. Kim, Bara & Yoo, Seung Han, 2021. "Population uncertainty and revealing contestants," Economics Letters, Elsevier, vol. 199(C).
    17. Yamashita, Takuro, 2018. "Optimal Public Information Disclosure by Mechanism Designer," TSE Working Papers 18-936, Toulouse School of Economics (TSE).
    18. Eduardo Perez-Richet, 2014. "Interim Bayesian Persuasion: First Steps," American Economic Review, American Economic Association, vol. 104(5), pages 469-474, May.
    19. Stegeman, Mark, 1996. "Participation Costs and Efficient Auctions," Journal of Economic Theory, Elsevier, vol. 71(1), pages 228-259, October.
    20. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    21. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    22. Skreta, Vasiliki & Koessler, Frédéric, 2021. "Information Design by an Informed Designer," CEPR Discussion Papers 15709, C.E.P.R. Discussion Papers.
    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. Skreta, Vasiliki & Koessler, Frédéric, 2021. "Information Design by an Informed Designer," CEPR Discussion Papers 15709, C.E.P.R. Discussion Papers.
    2. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    3. Frédéric Koessler & Vasiliki Skreta, 2023. "Informed Information Design," Journal of Political Economy, University of Chicago Press, vol. 131(11), pages 3186-3232.
    4. Diego Aycinena & Lucas Rentschler, 2018. "Auctions with endogenous participation and an uncertain number of bidders: experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 21(4), pages 924-949, December.
    5. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    6. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    7. Xin Zhao, 2023. "Auction design by an informed seller: A foundation of reserve price signalling," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(3), pages 1161-1190, August.
    8. Vasiliki Skreta, 2011. "On the informed seller problem: optimal information disclosure," Review of Economic Design, Springer;Society for Economic Design, vol. 15(1), pages 1-36, March.
    9. Roger B. Myerson, 1988. "Mechanism Design," Discussion Papers 796, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Xin Zhao, 2018. "Auction Design by an Informed Seller: The Optimality of Reserve Price Signaling," Working Paper Series 53, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    11. Markus Brunnermeier & Rohit Lamba & Carlos Segura-Rodriguez, 2020. "Inverse Selection," Working Papers 2020-50, Princeton University. Economics Department..
    12. Brocas, Isabelle, 2013. "Selling an asset to a competitor," European Economic Review, Elsevier, vol. 57(C), pages 39-62.
    13. Pierre Bernhard & Marc Deschamps, 2017. "On Dynamic Games with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 7(3), pages 360-385, September.
    14. Eduardo Perez‐Richet & Vasiliki Skreta, 2022. "Test Design Under Falsification," Econometrica, Econometric Society, vol. 90(3), pages 1109-1142, May.
    15. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    16. Kim, Bara & Yoo, Seung Han, 2021. "Population uncertainty and revealing contestants," Economics Letters, Elsevier, vol. 199(C).
    17. Celik, Gorkem & Yilankaya, Okan, 2017. "Resale in second-price auctions with costly participation," International Journal of Industrial Organization, Elsevier, vol. 54(C), pages 148-174.
    18. Marco Ottaviani & Andrea Prat, 2001. "The Value of Public Information in Monopoly," Econometrica, Econometric Society, vol. 69(6), pages 1673-1683, November.
    19. Dimitris Kostamis & Damian R. Beil & Izak Duenyas, 2009. "Total-Cost Procurement Auctions: Impact of Suppliers' Cost Adjustments on Auction Format Choice," Management Science, INFORMS, vol. 55(12), pages 1985-1999, December.
    20. Anastasios Dosis, 2022. "On the informed principal model with common values," RAND Journal of Economics, RAND Corporation, vol. 53(4), pages 792-825, December.

    More about this item

    Keywords

    informed principal; mechanism; population uncertainty; mechanical equivalence;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:iek:wpaper:2204. 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: Kim, Jisoo (email available below). General contact details of provider: https://edirc.repec.org/data/ierkukr.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.