Abstract
In this paper, we investigate the mean field games with K classes
of agents who are weakly coupled via the empirical measure. The
underlying dynamics of the representative agents is assumed to be a
controlled nonlinear Markov process associated with rather general
integro-differential generators of L´evy-Khintchine type (with variable
coefficients), with the major stress on applications to stable and stable-
like processes, as well as their various modifications like tempered
stable-like processes or their mixtures with diffusions. We show that
nonlinear measure-valued kinetic equations describing the dynamic
law of large numbers limit for system with large number N of agents
are solvable and that their solutions represent 1/N-Nash equilibria for
approximating systems of N agents.
of agents who are weakly coupled via the empirical measure. The
underlying dynamics of the representative agents is assumed to be a
controlled nonlinear Markov process associated with rather general
integro-differential generators of L´evy-Khintchine type (with variable
coefficients), with the major stress on applications to stable and stable-
like processes, as well as their various modifications like tempered
stable-like processes or their mixtures with diffusions. We show that
nonlinear measure-valued kinetic equations describing the dynamic
law of large numbers limit for system with large number N of agents
are solvable and that their solutions represent 1/N-Nash equilibria for
approximating systems of N agents.
Original language | English |
---|---|
Article number | 33 |
Pages (from-to) | 33 |
Number of pages | 65 |
Journal | Matematicheskaya Teoriya Igr i Ee Prilozheniya |
Volume | 5 |
Issue number | 4 |
Publication status | Published - 2013 |
Keywords
- stable-lilke processes
- kinetic equation
- forward-backward system
- dynamic law of large numbers
- rates of convergence
- tagged particle
- ε-Nash equilibrium