IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v62y2011i2p91-94.html
   My bibliography  Save this article

A family of identities related to zero-sum and team games

Author

Listed:
  • Stanford, William

Abstract

We list and prove a family of binomial identities by calculating in two ways the probabilities of approximate saddlepoints occurring in random mxn matrices. The identities are easily seen to be equivalent to the evaluation of a family of Gauss 2F1 polynomials according to a formula of Vandermonde. We also consider some implications concerning the number of approximate pure strategy Nash equilibria we can expect in large matrix zero-sum and team games.

Suggested Citation

  • Stanford, William, 2011. "A family of identities related to zero-sum and team games," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 91-94, September.
    • Handle: RePEc:eee:matsoc:v:62:y:2011:i:2:p:91-94
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489611000382
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
    2. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, 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. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Hannu Salonen, 2010. "On the existence of Nash equilibria in large games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 351-357, July.
    3. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," PSE Working Papers halshs-03735680, HAL.
    4. 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.
    5. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    7. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    8. Tolotti, Marco & Yepez, Jorge, 2020. "Hotelling-Bertrand duopoly competition under firm-specific network effects," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 105-128.
    9. Felix Bierbrauer, 2008. "Optimal Income Taxation, Public Goods Provision and Robust Mechanism Design," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2008_31, Max Planck Institute for Research on Collective Goods.
    10. Antonio Penta & Peio Zuazo-Garin, 2022. "Rationalizability, Observability, and Common Knowledge," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(2), pages 948-975.
    11. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    12. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    13. Blonski, Matthias & von Lilienfeld-Toal, Ulf, 2008. "Excess returns and the distinguished player paradox," University of Göttingen Working Papers in Economics 78, University of Goettingen, Department of Economics.
    14. Yaron Azrieli & Eran Shmaya, 2013. "Lipschitz Games," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 350-357, May.
    15. Carmona, Guilherme, 2008. "Purification of Bayesian-Nash equilibria in large games with compact type and action spaces," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1302-1311, December.
    16. Felix Bierbrauer, 2005. "Optimal Income Taxation and Public Good Provision in a Two-Class Economy," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2005_25, Max Planck Institute for Research on Collective Goods.
    17. Dequiedt, Vianney & Zenou, Yves, 2013. "International migration, imperfect information, and brain drain," Journal of Development Economics, Elsevier, vol. 102(C), pages 62-78.
    18. David P. Myatt, 2019. "A Theory of Stable Price Dispersion," Economics Series Working Papers 873, University of Oxford, Department of Economics.
    19. Edward Cartwright & Myrna Wooders, 2009. "On purification of equilibrium in Bayesian games and expost Nash equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 127-136, March.
    20. Felix Bierbrauer, 2006. "Collectively Incentive Compatible Tax Systems," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2006_24, Max Planck Institute for Research on Collective Goods.

    More about this item

    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:matsoc:v:62:y:2011:i:2:p:91-94. 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/505565 .

    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.