A nonzero-sum risk-sensitive stochastic differential game in the orthant

Mrinal K. Ghosh; Somnath Pradhan

doi:10.3934/mcrf.2021025

Article Contents

2022, Volume 12, Issue 2: 343-370. Doi: 10.3934/mcrf.2021025

This issue Previous Article Controllability under positive constraints for quasilinear parabolic PDEs Next Article Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems

A nonzero-sum risk-sensitive stochastic differential game in the orthant

Mrinal K. Ghosh^1, and
Somnath Pradhan^2, ,

1.
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
2.
Department of Mathematics, Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India

^* Corresponding author: Somnath Pradhan
^* Corresponding author: Somnath Pradhan

Received: July 2020

Revised: January 2021

Early access: April 2021

Published: June 2022

This work is partially supported by UGC Center for Advanced Study

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Abstract

We study a nonzero-sum risk-sensitive stochastic differential game for controlled reflecting diffusion processes in the nonnegative orthant. We treat two cost evaluation criteria, namely, discounted cost and ergodic cost. Under certain assumptions, we establish the existence of Nash equilibria. Also, we completely characterize a Nash equilibrium for the ergodic cost criterion in the space of stationary Markov strategies.

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Mathematics Subject Classification: Primary: 91A15; Secondary: 91A23.

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References

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