Ghosh, MK and Kumar, KS and Pal, C and Pradhan, S (2023) Nonzero-sum risk-sensitive stochastic differential games: A multi-parameter eigenvalue problem approach. In: Systems and Control Letters, 172 .
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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 Hamilton–Jacobi–Bellman (HJB) equations. Exploiting the stochastic representation of the principal eigenfunctions we completely characterize Nash equilibrium points in the space of stationary Markov strategies. The complete characterization of Nash equilibrium points is established under an additive structural assumption on the running cost and the drift term.
| Item Type: | Journal Article |
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| Publication: | Systems and Control Letters |
| Publisher: | Elsevier B.V. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Computation theory; Dynamic programming; Game theory; Stochastic systems, Eigenvalue problem; Hamilton Jacobi Bellman equation; Multiparameters; Nash equilibria; Nash equilibrium point; Parametric family; Parametric family of markov generator; Principal eigenvalues; Risk sensitive cost criteria; Stochastic differential game, Eigenvalues and eigenfunctions |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 02 Feb 2023 10:11 |
| Last Modified: | 02 Feb 2023 10:11 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79777 |
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