Journal of Dynamics and Games (JDG)

Tail probabilities for triangular arrays

Pages: 45 - 56, Volume 1, Issue 1, January 2014      doi:10.3934/jdg.2014.1.45

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Drew Fudenberg - Department of Economics, Harvard University, Littauer Center, 1805 Cambridge Street, Cambridge, MA 02138, United States (email)
David K. Levine - Department of Economics, Washington University in St. Louis, 1 Brookings Dr., St. Louis MO 63130-4899, United States (email)

Abstract: Different discrete time triangular arrays representing a noisy signal of players' activities can lead to the same limiting diffusion process yet lead to different 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.

Keywords:  Triangular array, tail probabilities, limit equilibria, continuous-time games.
Mathematics Subject Classification:  Primary: 60G50, 91A20; Secondary: 60B10, 91A25, 91B70.

Received: June 2012;      Revised: January 2013;      Available Online: June 2013.