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January  2014, 1(1): 45-56. doi: 10.3934/jdg.2014.1.45

Tail probabilities for triangular arrays

Drew Fudenberg 1, and  David K. Levine 2,

1. 

Department of Economics, Harvard University, Littauer Center, 1805 Cambridge Street, Cambridge, MA 02138, United States
2. 

Department of Economics, Washington University in St. Louis, 1 Brookings Dr., St. Louis MO 63130-4899, United States

Received  June 2012 Revised  January 2013 Published  June 2013

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: tail probabilities, Triangular array, continuous-time games., limit equilibria.
Mathematics Subject Classification: Primary: 60G50, 91A20; Secondary: 60B10, 91A25, 91B7.
Citation: Drew Fudenberg, David K. Levine. Tail probabilities for triangular arrays. Journal of Dynamics & Games, 2014, 1 (1) : 45-56. doi: 10.3934/jdg.2014.1.45
References:
[1]

W. Feller, "An Introduction to Probability Theory and Its Applications," Volume II, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971.  Google Scholar

[2]

D. Fudenberg and D. K. Levine, Continuous time limits of repeated games with imperfect public monitoring, Review of Economic Dynamics, 10 (2007), 173-192. Google Scholar

[3]

D. Fudenberg and D. K. Levine, Repeated games with frequent signals, Quarterly Journal of Economics, 124 (2009), 233-265. Google Scholar

[4]

J. A. Mirlees, Notes on welfare economics, information and uncertainty, in "Essays on Economic Behavior Under Uncertainty" (eds. M. Balch, D. McFadden and S.-Y. Wu), North Holland, Amsterdam, 1974. Google Scholar

[5]

Y. Sannikov, Games with imperfectly observed actions in continuous time, Econometrica, 75 (2007), 1285-1329. doi: 10.1111/j.1468-0262.2007.00795.x.  Google Scholar

[6]

Y. Sannikov and A. Skrzypacz, Impossibility of collusion under imperfect monitoring with flexible production, American Economic Review, 97 (2007), 1794-1823. Google Scholar

[7]

T. Sadzik and E. Stacchetti, Agency Models with Frequent Actions: A Quadratic Approximation Method, in "Workshop on Macroeconomic Applications of Dynamic Games and Contracts" (Stonybrook), (2012). Google Scholar

show all references

References:
[1]

W. Feller, "An Introduction to Probability Theory and Its Applications," Volume II, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971.  Google Scholar

[2]

D. Fudenberg and D. K. Levine, Continuous time limits of repeated games with imperfect public monitoring, Review of Economic Dynamics, 10 (2007), 173-192. Google Scholar

[3]

D. Fudenberg and D. K. Levine, Repeated games with frequent signals, Quarterly Journal of Economics, 124 (2009), 233-265. Google Scholar

[4]

J. A. Mirlees, Notes on welfare economics, information and uncertainty, in "Essays on Economic Behavior Under Uncertainty" (eds. M. Balch, D. McFadden and S.-Y. Wu), North Holland, Amsterdam, 1974. Google Scholar

[5]

Y. Sannikov, Games with imperfectly observed actions in continuous time, Econometrica, 75 (2007), 1285-1329. doi: 10.1111/j.1468-0262.2007.00795.x.  Google Scholar

[6]

Y. Sannikov and A. Skrzypacz, Impossibility of collusion under imperfect monitoring with flexible production, American Economic Review, 97 (2007), 1794-1823. Google Scholar

[7]

T. Sadzik and E. Stacchetti, Agency Models with Frequent Actions: A Quadratic Approximation Method, in "Workshop on Macroeconomic Applications of Dynamic Games and Contracts" (Stonybrook), (2012). Google Scholar

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