IDEAS home Printed from https://ideas.repec.org/p/pit/wpaper/6837.html
   My bibliography  Save this paper

Existence of Trembling hand perfect and sequential equilibrium in Stochastic Games

Author

Listed:
  • Sofia Moroni

Abstract

In this paper we define notions of trembling hand and sequential equilibrium and show that both types of equilibria exist in a large class of stochastic games that may feature incomplete and imperfect information. These equilibria do not necessitate the use of a public correlating device. Under further regularity assumptions each stochastic game has a sequence of approximating finite games whose equilibria approximate equilibria of the limit game.

Suggested Citation

  • Sofia Moroni, 2020. "Existence of Trembling hand perfect and sequential equilibrium in Stochastic Games," Working Paper 6837, Department of Economics, University of Pittsburgh.
    • Handle: RePEc:pit:wpaper:6837
    as

    Download full text from publisher

    File URL: https://www.econ.pitt.edu/sites/default/files/working_papers/WP.20.01.Web_.upload.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gensbittel, Fabien & Lovo, Stefano & Renault, Jérôme & Tomala, Tristan, 2018. "Zero-sum revision games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 504-522.
    2. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    3. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    4. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    5. Sofia Moroni, 2018. "Games with Private Timing," Working Paper 6400, Department of Economics, University of Pittsburgh.
    6. Hugo Hopenhayn & Maryam Saeedi, 2016. "Bidding Dynamics in Auctions," NBER Working Papers 22716, National Bureau of Economic Research, Inc.
    7. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    8. Sofia Moroni, 2016. "Sniping in Proxy Auctions with Deadlines," Working Paper 5875, Department of Economics, University of Pittsburgh.
    9. Alvin E. Roth & Axel Ockenfels, 2002. "Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet," American Economic Review, American Economic Association, vol. 92(4), pages 1093-1103, September.
    10. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2016. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 889-931.
    11. Ockenfels, Axel & Roth, Alvin E., 2006. "Late and multiple bidding in second price Internet auctions: Theory and evidence concerning different rules for ending an auction," Games and Economic Behavior, Elsevier, vol. 55(2), pages 297-320, May.
    12. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    13. Stinchcombe, Maxwell B., 2011. "Correlated equilibrium existence for infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 638-655, March.
    14. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    15. 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.
    16. Attila Ambrus & James Burns & Yuhta Ishii, 2012. "Gradual Bidding in eBay-Like Auctions," Working Papers 12-12, Duke University, Department of Economics.
    17. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
    18. Lovo , Stefano & Tomala , Tristan, 2015. "Markov Perfect Equilibria in Stochastic Revision Games," HEC Research Papers Series 1093, HEC Paris.
    19. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    20. , & , & , & ,, 2014. "Asynchronicity and coordination in common and opposing interest games," Theoretical Economics, Econometric Society, vol. 9(2), May.
    21. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
    22. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    23. Manelli, Alejandro M, 1996. "Cheap Talk and Sequential Equilibria in Signaling Games," Econometrica, Econometric Society, vol. 64(4), pages 917-942, July.
    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. Sofia Moroni, 2019. "Existence of trembling hand perfect and sequential equilibrium in games with stochastic timing of moves," Working Paper 6757, Department of Economics, University of Pittsburgh.
    2. Stinchcombe, Maxwell B., 2011. "Balance and discontinuities in infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 656-671, March.
    3. Zhuohan Wang & Dong Hao, 2022. "Characterizing Agent Behavior in Revision Games with Uncertain Deadline," Games, MDPI, vol. 13(6), pages 1-13, November.
    4. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    5. 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.
    6. Yuhki Hosoya & Chaowen Yu, 2022. "On the approximate purification of mixed strategies in games with infinite action sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 69-93, May.
    7. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    8. Duggan, John, 2017. "Existence of stationary bargaining equilibria," Games and Economic Behavior, Elsevier, vol. 102(C), pages 111-126.
    9. Stinchcombe, Maxwell B., 2011. "Correlated equilibrium existence for infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 638-655, March.
    10. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    11. Sofia Moroni, 2016. "Sniping in Proxy Auctions with Deadlines," Working Paper 5875, Department of Economics, University of Pittsburgh.
    12. Anna Jaśkiewicz & Andrzej S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.
    13. Yuichiro Kamada & Michihiro Kandori, 2020. "Revision Games," Econometrica, Econometric Society, vol. 88(4), pages 1599-1630, July.
    14. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    15. Page, Frank, 2016. "Stationary Markov equilibria for approximable discounted stochastic games," LSE Research Online Documents on Economics 67808, London School of Economics and Political Science, LSE Library.
    16. Barelli, Paulo & Duggan, John, 2015. "Purification of Bayes Nash equilibrium with correlated types and interdependent payoffs," Games and Economic Behavior, Elsevier, vol. 94(C), pages 1-14.
    17. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    18. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," NBER Working Papers 29291, National Bureau of Economic Research, Inc.
    19. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    20. Dong Hao & Qi Shi & Jinyan Su & Bo An, 2021. "Cooperation, Retaliation and Forgiveness in Revision Games," Papers 2112.02271, arXiv.org, revised Oct 2022.

    More about this item

    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:pit:wpaper:6837. 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: Department of Economics, University of Pittsburgh (email available below). General contact details of provider: https://edirc.repec.org/data/depghus.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.