Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909294076624896 |
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| author | Bose, Bivakar Pal, Chandan Pradhan, Somnath Saha, Subhamay |
| author_facet | Bose, Bivakar Pal, Chandan Pradhan, Somnath Saha, Subhamay |
| contents | In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated ergodic optimality equations admit unique solutions. Finally, the existence of Nash-equilibrium in randomized stationary strategies is established by showing that an appropriate set-valued map has a fixed point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion Bose, Bivakar Pal, Chandan Pradhan, Somnath Saha, Subhamay Optimization and Control Probability 91A15, 91A50 In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated ergodic optimality equations admit unique solutions. Finally, the existence of Nash-equilibrium in randomized stationary strategies is established by showing that an appropriate set-valued map has a fixed point. |
| title | Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion |
| topic | Optimization and Control Probability 91A15, 91A50 |
| url | https://arxiv.org/abs/2408.12849 |