Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

By Vassili N. Kolokoltsov. 2012

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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.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/364a924f99b6359a12e33b515bcc6223a915d012