IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4782.html
   My bibliography  Save this article

Value-based distance between information structures

Author

Listed:
  • Gensbittel, Fabien

    (Toulouse School of economics)

  • Pęski, Marcin

    (University of Toronto)

  • Renault, Jérôme

    (TSE (Université Toulouse 1 Capitole))

Abstract

We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of information in games versus single-agent problems, the value of additional information, informational substitutes, complements, or joint information. The convergence to a countable information structure under value-based distance is equivalent to the weak convergence of belief hierarchies, implying, among other things, that for zero-sum games, approximate knowledge is equivalent to common knowledge. At the same time, the space of information structures under the value-based distance is large: there exists a sequence of information structures where players acquire increasingly more information, and \varepsilon>0 such that any two elements of the sequence have distance of at least \varepsilon. This result answers by the negative the second (and last unsolved) of the three problems posed by J.F. Mertens in his paper “Repeated Games”, ICM 1986.

Suggested Citation

  • Gensbittel, Fabien & Pęski, Marcin & Renault, Jérôme, 2022. "Value-based distance between information structures," Theoretical Economics, Econometric Society, vol. 17(3), July.
  • Handle: RePEc:the:publsh:4782
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20221225/34325/1014
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. , & , & , & ,, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
    2. Olivier GOSSNER & Jean-François MERTENS, 2020. "The Value of Information in Zero-Sum Games," Working Papers 2020-19, Center for Research in Economics and Statistics.
    3. Dov Monderer & Dov Samet, 1996. "Proximity of Information in Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 707-725, August.
    4. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    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. Fabien Gensbittel & Marcin Peski & Jérôme Renault, 2021. "Value-Based Distance Between Information Structures," Working Papers hal-01869139, HAL.
    2. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2012. "The Strategic Impact of Higher-Order Beliefs," Levine's Working Paper Archive 786969000000000517, David K. Levine.
    3. Kets, Willemien, 2011. "Robustness of equilibria in anonymous local games," Journal of Economic Theory, Elsevier, vol. 146(1), pages 300-325, January.
    4. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2017. "Characterizing the Strategic Impact of Misspecified Beliefs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(4), pages 1424-1471.
    5. Yuhki Hosoya & Chaowen Yu, 2021. "On the Approximate Purification of Mixed Strategies in Games with Infinite Action Sets," Papers 2103.07736, arXiv.org, revised Apr 2022.
    6. Oriol Carbonell-Nicolau, 2015. "Semicontinuous integrands as jointly measurable maps," Departmental Working Papers 201512, Rutgers University, Department of Economics.
    7. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    8. Chen, Yi-Chun & Mueller-Frank, Manuel & Pai, Mallesh M., 2022. "Continuous implementation with direct revelation mechanisms," Journal of Economic Theory, Elsevier, vol. 201(C).
    9. Eric J. Hoffmann & Tarun Sabarwal, 2019. "Equilibrium existence in global games with general payoff structures," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 105-115, May.
    10. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    11. Qin, Cheng-Zhong & Yang, Chun-Lei, 2009. "An Explicit Approach to Modeling Finite-Order Type Spaces and Applications," University of California at Santa Barbara, Economics Working Paper Series qt8hq7j89k, Department of Economics, UC Santa Barbara.
    12. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2016. "Behavioral perfect equilibrium in Bayesian games," Games and Economic Behavior, Elsevier, vol. 98(C), pages 78-109.
    13. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    14. , & , & , & ,, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
    15. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    16. , & ,, 2017. "Bayesian games with a continuum of states," Theoretical Economics, Econometric Society, vol. 12(3), September.
    17. Germano, Fabrizio & Weinstein, Jonathan & Zuazo-Garin, Peio, 2020. "Uncertain rationality, depth of reasoning and robustness in games with incomplete information," Theoretical Economics, Econometric Society, vol. 15(1), January.
    18. Michael Greinecker & Christoph Kuzmics, 2019. "Limit Orders under Knightian Uncertainty," Graz Economics Papers 2019-03, University of Graz, Department of Economics.
    19. Kets, W., 2008. "Beliefs in Network Games (Revised version of CentER DP 2007-46)," Other publications TiSEM a08e38fd-6b00-4233-94ce-3, Tilburg University, School of Economics and Management.
    20. Ori Haimanko, 2021. "Bayesian Nash equilibrium existence in (almost continuous) contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1231-1258, April.

    More about this item

    Keywords

    Value of information; universal type space;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    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:the:publsh:4782. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.