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

Tail probabilities for triangular arrays

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.
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, (1971).

[2]

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

[3]

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

[4]

J. A. Mirlees, Notes on welfare economics, information and uncertainty,, in, (1974).

[5]

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

[6]

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

[7]

T. Sadzik and E. Stacchetti, Agency Models with Frequent Actions: A Quadratic Approximation Method,, in, (2012).

show all references

References:
[1]

W. Feller, "An Introduction to Probability Theory and Its Applications,", Volume II, (1971).

[2]

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

[3]

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

[4]

J. A. Mirlees, Notes on welfare economics, information and uncertainty,, in, (1974).

[5]

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

[6]

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

[7]

T. Sadzik and E. Stacchetti, Agency Models with Frequent Actions: A Quadratic Approximation Method,, in, (2012).

[1]

Joon Kwon, Panayotis Mertikopoulos. A continuous-time approach to online optimization. Journal of Dynamics & Games, 2017, 4 (2) : 125-148. doi: 10.3934/jdg.2017008

[2]

Hanqing Jin, Xun Yu Zhou. Continuous-time portfolio selection under ambiguity. Mathematical Control & Related Fields, 2015, 5 (3) : 475-488. doi: 10.3934/mcrf.2015.5.475

[3]

Fritz Colonius, Guilherme Mazanti. Decay rates for stabilization of linear continuous-time systems with random switching. Mathematical Control & Related Fields, 2018, 8 (0) : 1-20. doi: 10.3934/mcrf.2019002

[4]

Hui Meng, Fei Lung Yuen, Tak Kuen Siu, Hailiang Yang. Optimal portfolio in a continuous-time self-exciting threshold model. Journal of Industrial & Management Optimization, 2013, 9 (2) : 487-504. doi: 10.3934/jimo.2013.9.487

[5]

Lakhdar Aggoun, Lakdere Benkherouf. A Markov modulated continuous-time capture-recapture population estimation model. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057

[6]

Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial & Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283

[7]

Willem Mélange, Herwig Bruneel, Bart Steyaert, Dieter Claeys, Joris Walraevens. A continuous-time queueing model with class clustering and global FCFS service discipline. Journal of Industrial & Management Optimization, 2014, 10 (1) : 193-206. doi: 10.3934/jimo.2014.10.193

[8]

Haixiang Yao, Zhongfei Li, Xun Li, Yan Zeng. Optimal Sharpe ratio in continuous-time markets with and without a risk-free asset. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1273-1290. doi: 10.3934/jimo.2016072

[9]

Alexander J. Zaslavski. Structure of approximate solutions of dynamic continuous time zero-sum games. Journal of Dynamics & Games, 2014, 1 (1) : 153-179. doi: 10.3934/jdg.2014.1.153

[10]

Mathias Staudigl, Jan-Henrik Steg. On repeated games with imperfect public monitoring: From discrete to continuous time. Journal of Dynamics & Games, 2017, 4 (1) : 1-23. doi: 10.3934/jdg.2017001

[11]

Juan Pablo Maldonado López. Discrete time mean field games: The short-stage limit. Journal of Dynamics & Games, 2015, 2 (1) : 89-101. doi: 10.3934/jdg.2015.2.89

[12]

Sylvain Sorin, Cheng Wan. Finite composite games: Equilibria and dynamics. Journal of Dynamics & Games, 2016, 3 (1) : 101-120. doi: 10.3934/jdg.2016005

[13]

Yinghua Dong, Yuebao Wang. Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums. Journal of Industrial & Management Optimization, 2011, 7 (4) : 849-874. doi: 10.3934/jimo.2011.7.849

[14]

Jean-Bernard Baillon, Guillaume Carlier. From discrete to continuous Wardrop equilibria. Networks & Heterogeneous Media, 2012, 7 (2) : 219-241. doi: 10.3934/nhm.2012.7.219

[15]

Ángel Arroyo, Joonas Heino, Mikko Parviainen. Tug-of-war games with varying probabilities and the normalized p(x)-laplacian. Communications on Pure & Applied Analysis, 2017, 16 (3) : 915-944. doi: 10.3934/cpaa.2017044

[16]

Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical approximation of continuous traffic congestion equilibria. Networks & Heterogeneous Media, 2009, 4 (3) : 605-623. doi: 10.3934/nhm.2009.4.605

[17]

Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír  Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803

[18]

Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics & Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002

[19]

Yutaka Sakuma, Atsushi Inoie, Ken’ichi Kawanishi, Masakiyo Miyazawa. Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time. Journal of Industrial & Management Optimization, 2011, 7 (3) : 593-606. doi: 10.3934/jimo.2011.7.593

[20]

Francisco Balibrea, J.L. García Guirao, J.I. Muñoz Casado. A triangular map on $I^{2}$ whose $\omega$-limit sets are all compact intervals of $\{0\}\times I$. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 983-994. doi: 10.3934/dcds.2002.8.983

 Impact Factor: 

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]