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Tail Probabilities for Triangular Arrays

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  • Drew Fudenberg
  • David K Levine

Abstract

Di erent discrete time triangular arrays representing a noisy signal of players' activities can lead to the same limiting di usion process yet lead to di erent limit equilibria. Whether the limit equilibria are equilibria of the limiting continuous time game depends on the limit properties of test statistics for whether a player has deviated. We provide an estimate of the tail probabilities along these arrays that allows us to determine the asymptotic behavior of the best test and thus of the best equilibrium.
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  • Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
  • Handle: RePEc:cla:levarc:786969000000000685
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    1. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    2. Drew Fudenberg & David K. Levine, 2008. "Continuous time limits of repeated games with imperfect public monitoring," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 17, pages 369-388 World Scientific Publishing Co. Pte. Ltd..
    3. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, September.
    4. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, Oxford University Press, vol. 124(1), pages 233-265.
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