Ghosh, MK and Golui, S and Pal, C and Pradhan, S (2022) Nonzero-Sum Risk-Sensitive Continuous-Time Stochastic Games with Ergodic Costs. In: Applied Mathematics and Optimization, 86 (1).
|
PDF
app_mat_opt_86-1_2022.pdf - Published Version Download (527kB) | Preview |
Abstract
We study nonzero-sum stochastic games for continuous time Markov decision processes on a denumerable state space with risk-sensitive ergodic cost criterion. Transition rates and cost rates are allowed to be unbounded. Under a Lyapunov type stability assumption, we show that the corresponding system of coupled HJB equations admits a solution which leads to the existence of a Nash equilibrium in stationary strategies. We establish this using an approach involving principal eigenvalues associated with the HJB equations. Furthermore, exploiting appropriate stochastic representation of principal eigenfunctions, we completely characterize Nash equilibria in the space of stationary Markov strategies. '
| Item Type: | Journal Article |
|---|---|
| Publication: | Applied Mathematics and Optimization |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the Author(s). |
| Keywords: | Continuous time systems; Eigenvalues and eigenfunctions; Fixed point arithmetic; Game theory; Markov processes; Stochastic systems, Cost criteria; Coupled HJB equation; Ergodics; Fan�s fixed point theorem; Fixed points theorems; HJB equations; Nash equilibria; Nonzero-sum game; Risk-sensitive ergodic cost criteria; Stationary strategy, Computation theory |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 19 Sep 2022 08:37 |
| Last Modified: | 19 Sep 2022 08:37 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76592 |
Actions (login required)
 |
View Item |
