On Mean Field Games with Common Noise based on Stable-Like Processes

  • Vassili N. Kolokoltsov University of Warwick
  • Marianna Troeva North-Eastern Federal University
DOI: https://doi.org/10.19139/soic.v7i2.637
Keywords: Mean-field games with common noise, Stable-like processes, McKean-Vlasov SPDE, Regularity, Sensitivity, Nash equilibrium

Abstract

In this paper, we study Mean Field games with common noise based on nonlinear stable-like processes. The MFG limit is specified by a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. The main result is that any its solution provides an 1/N-Nash equilibrium for the initial game of N agents. Our approach is based on interpreting the common noise as a kind of binary interaction of agents and our previous results on regularity and sensitivity with respect to the initial conditions of the solution to the nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes.

Author Biographies

Vassili N. Kolokoltsov, University of Warwick
Department of Statistics, Professor
Marianna Troeva, North-Eastern Federal University
Research Institute of Mathematics, Dr

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Published
2019-05-17
How to Cite
Kolokoltsov, V. N., & Troeva, M. (2019). On Mean Field Games with Common Noise based on Stable-Like Processes. Statistics, Optimization & Information Computing, 7(2), 264-276. https://doi.org/10.19139/soic.v7i2.637
Issue
Vol 7 No 2 (2019)
Section
Research Articles
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