- Previous Article
- JDG Home
- This Issue
-
Next Article
Discrete time mean field games: The short-stage limit
Reversibility and oscillations in zero-sum discounted stochastic games
1. | Sorbonne Universités, UPMC Univ Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, F-75005, Paris, France |
2. | Université Paris-Dauphine, CEREMADE, Place du Maréchal De Lattre de Tassigny, 75775 Paris cedex 16, France |
References:
[1] |
T. Bewley and E. Kohlberg, On stochastic games with stationary optimal strategies,, Mathematics of Operations Research, 3 (1978), 104.
doi: 10.1287/moor.3.2.104. |
[2] |
J. Bolte, S. Gaubert and G. Vigeral, Definable zero-sum stochastic games,, Mathematics of Operation Research, 40 (2015), 171.
doi: 10.1287/moor.2014.0666. |
[3] |
G. Grimmett and D. Stirzaker, Probability and Random Processes,, Oxford University Press, (2001).
|
[4] |
R. Laraki, Explicit formulas for repeated games with absorbing states,, International Journal of Game Theory, 39 (2010), 53.
doi: 10.1007/s00182-009-0193-2. |
[5] |
J.-F. Mertens, A. Neyman and D. Rosenberg, Absorbing games with compact action spaces,, Mathematics of Operation Research, 34 (2009), 257.
doi: 10.1287/moor.1080.0372. |
[6] |
J.-F. Mertens, S. Sorin and S. Zamir, Repeated Games,, Cambridge University Press, (2015). Google Scholar |
[7] |
A. Neyman, Stochastic games and nonexpansive maps,, in Stochastic Games and Applications (eds. A. Neyman and S. Sorin), (2003), 397.
doi: 10.1007/978-94-010-0189-2_26. |
[8] |
D. Rosenberg and S. Sorin, An operator approach to zero-sum repeated games,, Israel Journal of Mathematics, 121 (2001), 221.
doi: 10.1007/BF02802505. |
[9] |
S. Sorin, A First Course on Zero-SumRepeated Games,, Springer-Verlag, (2002).
|
[10] |
S. Sorin, The operator approach to zero-sum stochastic games,, in Stochastic Games and Applications (eds. A. Neyman and S. Sorin), (2003), 417.
|
[11] |
S. Sorin and G. Vigeral, Existence of the limit value of two person zero-sum discounted repeated games via comparison theorems,, Journal of Opimization Theory and Applications, 157 (2013), 564.
doi: 10.1007/s10957-012-0193-4. |
[12] |
G. Vigeral, A zero-sum stochastic game with compact action sets and no asymptotic value,, Dynamic Games and Applications, 3 (2013), 172.
doi: 10.1007/s13235-013-0073-z. |
[13] |
B. Ziliotto, Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture maxmin=$\lim v_n$,, to appear in Annals of Probability, (2013). Google Scholar |
show all references
References:
[1] |
T. Bewley and E. Kohlberg, On stochastic games with stationary optimal strategies,, Mathematics of Operations Research, 3 (1978), 104.
doi: 10.1287/moor.3.2.104. |
[2] |
J. Bolte, S. Gaubert and G. Vigeral, Definable zero-sum stochastic games,, Mathematics of Operation Research, 40 (2015), 171.
doi: 10.1287/moor.2014.0666. |
[3] |
G. Grimmett and D. Stirzaker, Probability and Random Processes,, Oxford University Press, (2001).
|
[4] |
R. Laraki, Explicit formulas for repeated games with absorbing states,, International Journal of Game Theory, 39 (2010), 53.
doi: 10.1007/s00182-009-0193-2. |
[5] |
J.-F. Mertens, A. Neyman and D. Rosenberg, Absorbing games with compact action spaces,, Mathematics of Operation Research, 34 (2009), 257.
doi: 10.1287/moor.1080.0372. |
[6] |
J.-F. Mertens, S. Sorin and S. Zamir, Repeated Games,, Cambridge University Press, (2015). Google Scholar |
[7] |
A. Neyman, Stochastic games and nonexpansive maps,, in Stochastic Games and Applications (eds. A. Neyman and S. Sorin), (2003), 397.
doi: 10.1007/978-94-010-0189-2_26. |
[8] |
D. Rosenberg and S. Sorin, An operator approach to zero-sum repeated games,, Israel Journal of Mathematics, 121 (2001), 221.
doi: 10.1007/BF02802505. |
[9] |
S. Sorin, A First Course on Zero-SumRepeated Games,, Springer-Verlag, (2002).
|
[10] |
S. Sorin, The operator approach to zero-sum stochastic games,, in Stochastic Games and Applications (eds. A. Neyman and S. Sorin), (2003), 417.
|
[11] |
S. Sorin and G. Vigeral, Existence of the limit value of two person zero-sum discounted repeated games via comparison theorems,, Journal of Opimization Theory and Applications, 157 (2013), 564.
doi: 10.1007/s10957-012-0193-4. |
[12] |
G. Vigeral, A zero-sum stochastic game with compact action sets and no asymptotic value,, Dynamic Games and Applications, 3 (2013), 172.
doi: 10.1007/s13235-013-0073-z. |
[13] |
B. Ziliotto, Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture maxmin=$\lim v_n$,, to appear in Annals of Probability, (2013). Google Scholar |
[1] |
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 |
[2] |
Marco Cirant, Diogo A. Gomes, Edgard A. Pimentel, Héctor Sánchez-Morgado. On some singular mean-field games. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021006 |
[3] |
Olena Naboka. On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1933-1956. doi: 10.3934/cpaa.2009.8.1933 |
[4] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[5] |
Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109 |
[6] |
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 |
[7] |
Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024 |
[8] |
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021035 |
[9] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[10] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[11] |
Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang. Emergent collective behaviors of stochastic kuramoto oscillators. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1059-1081. doi: 10.3934/dcdsb.2019208 |
[12] |
María J. Garrido-Atienza, Bohdan Maslowski, Jana Šnupárková. Semilinear stochastic equations with bilinear fractional noise. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3075-3094. doi: 10.3934/dcdsb.2016088 |
[13] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[14] |
Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2693-2719. doi: 10.3934/dcdsb.2020201 |
[15] |
Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192 |
[16] |
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 |
[17] |
Longxiang Fang, Narayanaswamy Balakrishnan, Wenyu Huang. Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021004 |
[18] |
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 |
[19] |
Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 |
[20] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]