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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

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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:
DateEvent
1 May 2012Published
27 February 2012Accepted
13 February 2012Submitted
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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