English

Nonzero-Sum Risk-Sensitive Stochastic Differential Games: A Multi-parameter Eigenvalue Problem Approach

Optimization and Control 2022-06-27 v1

Abstract

We study nonzero-sum stochastic differential games with risk-sensitive ergodic cost criterion. Under certain conditions, using multi-parameter eigenvalue approach, we establish the existence of a Nash equilibrium in the space of stationary Markov strategies. We achieve our results by studying the relevant systems of coupled HJB equations. Exploiting the stochastic representation of the principal eigenfunctions we completely characterize Nash equilibrium points in the space of stationary Markov strategies.

Keywords

Cite

@article{arxiv.2206.12067,
  title  = {Nonzero-Sum Risk-Sensitive Stochastic Differential Games: A Multi-parameter Eigenvalue Problem Approach},
  author = {Mrinal K. Ghosh and K. Suresh Kumar and Chandan Pal and Somnath Pradhan},
  journal= {arXiv preprint arXiv:2206.12067},
  year   = {2022}
}
R2 v1 2026-06-24T12:02:38.861Z