LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2012)
Publisher: Canadian Center of Science and Education
Languages: English
Types: Article
Subjects: QA
Managing large complex stochastic systems, including competitive interests, when one or several players can control the behavior of a large number of particles (agents, mechanisms, vehicles, subsidiaries, species, police units, etc), say Nk for a player k, the complexity of the game-theoretical (or Markov decision) analysis can become immense as Nk → ∞. However, under rather general assumptions, the limiting problem as all Nk → ∞ can be described by a well manageable deterministic evolution. In this paper we analyze some simple situations of this kind proving the convergence of Nashequilibria for finite games to equilibria of a limiting deterministic differential game.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Andersson, D., & Djehiche, B. (2011). A maximum principle for SDEs of mean-field type. Appl. Math. Optim., 63, 341-356. http://dx.doi.org/10.1007/s00245-010-9123-8 Belavkin, V. P., & Kolokoltsov, V. N. (2003). On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. Royal Soc. Lond. A, 459, 727-748. http://dx.doi.org/10.1098/rspa.2002.1026 Bogolyubov, N. N. (1946). Problems of the dynamic theory in statistical physics. Moscow, Nauka (in Russian).
    • Bordenave, C., McDonald, D., & Proutiere A. (2007). A particle system in interaction with a rapidly varying environment: Mean field limits and applications.
    • Buckdahn, R., Djehiche, B., Li, J., & Peng, S. (2009). Mean-field backward stochastic differential equations: a limit approach. Ann. Prob, 37, 1524-1565. http://dx.doi.org/10.1214/08-AOP442 Case, J. H. (1967). Toward a Theory of Many Player Differential Games. SIAM Journal on Control, 7, 179-197.
    • http://dx.doi.org/10.1137/0307013 Darling, R. W. R., & Norris, J. R. (2008). Differential equation approximations for Markov chains. Probab. Surv., 5, 3779.
    • Kushner, H. J. (2002). Numerical approximations for stochastic differential games. SIAM Journal of Control and Optimization, 41, 457-486. http://dx.doi.org/10.1137/S0363012901389457 Kushner, H. J., & Dupuis, P. (2001). Numerical methods for stochastic control problems in continuous time. 2ed., New York: Springer.
    • Lasry, J.-M., & Lions, L. Jeux Champ Moyen. C. R. Math. Acad. Sci. Paris, 343, 619-625 and 679-684.
    • Le Boudec, J.-Y., McDonald, D., & Mundinger, J. (2007). A Generic Mean Field Convergence Result for Systems of Interacting Objects. QEST 2007 (4th INternationalConference on Quantitative Evaluation of SysTems), 3-18.
    • Leontovich, M. A. (1935). Main equations of the kinetic theory from the point of view of random processes. Journal of Experimantal and Theoretical Physics , 5, 211-231.
    • Malafeyev, O. A. (2000). Controlled conflict systems (In Russian). St. Petersburg State University Publication, ISBN 5-288-01769-7.
    • Maslov, V. P., & Tariverdiev, C. E. (1982). Asymptotics of the Kolmogorov-Feller equation for systems with the large number of particles. Itogi Nauki i Techniki. Teoriya veroyatnosti, v.19, VINITI, Moscow (in Russian), 85-125.
    • Bena¨ım, M., & Le Boudec, J.-Y. (2008). A class of mean field interaction models for computer and communication systems. Performance Evaluation, 65, 823-838. http://dx.doi.org/10.1016/j.peva.2008.03.005 Bena¨ım, M., & Weibull, J. (2003). Deterministoc approximation of stochastic evolution in games. Econometrica, 71, 873-903. http://dx.doi.org/10.1111/1468-0262.00429 McEneaney, W. (2006). Max-plus methods for nonlinear control and estimation. Systems and Control: Foundations and Applications. Boston, MA: Birkha¨user Boston, Inc.
    • Milutinovic, D., & Lima, P. (2006). Modeling and Optimal Centralized Control of a Large-Size Robotic Population.
    • Robotics, IEEE Transactions on Robotics, 22, 1280-1285. http://dx.doi.org/10.1109/TRO.2006.882941 Olsder, G. J. (2001). On open- and closed-loop bang-bang control in nonzero-sum differential games. SIAM J. Control Optim., 40, 1087-1106. http://dx.doi.org/10.1137/S0363012900373252 Petrosjan, L. A., & Zenkevich, N. A. (1996). Game Theory, World Scientific, Singapore.
    • Ramasubraanian, S. (2007). A d-person Differential Game with State Space Constraints. Appl. Math. Optim., 56, 312-342. http://dx.doi.org/10.1007/s00245-007-9011-z Song, Q. S. (2008). Convergence of Markov chain approximation on generalized HJB equation and its applications.
    • Automatica J. IFAC, 44, 761-766. http://dx.doi.org/10.1016/j.automatica.2007.07.014 Tolwinski, B., Haurie, A., & Leitmann, G. (1986). Cooperative Equilibra in Differential Games. J. Math. Anal. Appl., 119, 182-202. http://dx.doi.org/10.1016/0022-247X(86)90152-6 Zak, M. (2000). Quantum Evolution as a Nonlinear Markov Process. Foundations of Physics Letters, 15, 229-243.
    • http://dx.doi.org/10.1023/A:1021079403550
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article