IDEAS home Printed from https://ideas.repec.org/p/hit/econdp/2007-02.html
   My bibliography  Save this paper

Uniform Continuity of the Value of Zero-Sum Games with Differential Information

Author

Listed:
  • Einy, Ezra
  • Haimanko, Ori
  • Moreno, Diego
  • Shitovitz, Benyamin

Abstract

We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan (1971) pseudo-metric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change, even with the weak topology on players' strategy sets.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, 2007. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Discussion Papers 2007-02, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2007-02
    Note: Revised version of Discussion Paper # 04-04 of Monaster Center for Economic Research, Ben-Gurion University of the Negev.
    as

    Download full text from publisher

    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/16956/070econDP07-02.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    2. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 793-812, November.
    3. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    4. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
    5. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    6. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
    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. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2008. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 552-560, August.
    2. Timothy Van Zandt & Kaifu Zhang, 2011. "A theorem of the maximin and applications to Bayesian zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 289-308, May.
    3. Barbie, Martin & Gupta, Abhishek, 2014. "The topology of information on the space of probability measures over Polish spaces," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 98-111.
    4. Khan, M. Ali & Sun, Yeneng & Tourky, Rabee & Zhang, Zhixiang, 2008. "Similarity of differential information with subjective prior beliefs," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 1024-1039, September.
    5. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 793-812, November.
    6. João Correia-da-Silva & Carlos Hervés-Beloso, 2007. "Private Information: Similarity as Compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 395-407, March.
    7. 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.
    8. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    9. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    10. Kets, W., 2007. "Convergence of Beliefs in Bayesian Network Games," Other publications TiSEM 372c88bd-4b09-4976-a6e2-4, Tilburg University, School of Economics and Management.
    11. Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    12. Hellwig, Christian, 2002. "Public Information, Private Information, and the Multiplicity of Equilibria in Coordination Games," Journal of Economic Theory, Elsevier, vol. 107(2), pages 191-222, December.
    13. Ezra Einy & Ori Haimanko & Biligbaatar Tumendemberel, 2012. "Continuity of the value and optimal strategies when common priors change," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 829-849, November.
    14. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 215-230, May.
    15. Jackson, Matthew O. & Rodriguez-Barraquer, Tomas & Tan, Xu, 2012. "Epsilon-equilibria of perturbed games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 198-216.
    16. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
    17. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    18. Beissner, Patrick & Tölle, Jonas, 2018. "A Compact Topology for Sigma-Algebra Convergence," Rationality and Competition Discussion Paper Series 74, CRC TRR 190 Rationality and Competition.
    19. Kets, W., 2007. "Beliefs in Network Games (Replaced by CentER DP 2008-05)," Other publications TiSEM 1c11352b-a9fb-4e2f-9bb0-d, Tilburg University, School of Economics and Management.
    20. Ulrich Schwalbe, 1999. "The core of an exchange economy with asymmetric information," Journal of Economics, Springer, vol. 70(2), pages 155-185, June.

    More about this item

    Keywords

    Zero-Sum Games; Differential Information; Value; Op-timal Strategies; Uniform Continuity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:hit:econdp:2007-02. 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: Digital Resources Section, Hitotsubashi University Library (email available below). General contact details of provider: https://edirc.repec.org/data/fehitjp.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.