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Existence of Trembling hand perfect and sequential equilibrium in Stochastic Games

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  • 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.

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  • 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
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    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., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    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. 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.
    19. Lovo , Stefano & Tomala , Tristan, 2015. "Markov Perfect Equilibria in Stochastic Revision Games," HEC Research Papers Series 1093, HEC Paris.
    20. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    21. , & , & , & ,, 2014. "Asynchronicity and coordination in common and opposing interest games," Theoretical Economics, Econometric Society, vol. 9(2), May.
    22. 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.
    23. 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.
    24. Manelli, Alejandro M, 1996. "Cheap Talk and Sequential Equilibria in Signaling Games," Econometrica, Econometric Society, vol. 64(4), pages 917-942, July.
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