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Nonlinear Markov games on a finite state space (mean-field and binary interactions)
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Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2012) Nonlinear Markov games on a finite state space (mean-field and binary interactions). International Journal of Statistics and Probability, Volume 1 (Number 1). doi:10.5539/ijsp.v1n1p77 ISSN 1927-7032.
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Official URL: http://dx.doi.org/10.5539/ijsp.v1n1p77
Abstract
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.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes | ||||||||
| Journal or Publication Title: | International Journal of Statistics and Probability | ||||||||
| Publisher: | Canadian Center of Science and Education | ||||||||
| ISSN: | 1927-7032 | ||||||||
| Official Date: | 1 May 2012 | ||||||||
| Dates: |
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| Volume: | Volume 1 | ||||||||
| Number: | Number 1 | ||||||||
| DOI: | 10.5539/ijsp.v1n1p77 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 28 July 2016 | ||||||||
| Date of first compliant Open Access: | 28 July 2016 | ||||||||
| Funder: | United States. Air Force. Office of Scientific Research (AFOSR), Rossiĭskai͡a akademii͡a nauk. Institute of Informatics Problems (IPI RAN) | ||||||||
| Grant number: | FA9550-09-1-0664 (AFOSR) |
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