On Stochastic Games with Multiple Objectives
We study two-player stochastic games, where the goal of one player is to satisfy a formula given as a boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and veri cation of open systems with...
| Main Authors: | , , , , |
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| Formato: | Report |
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DCS
2013
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| _version_ | 1826296418184200192 |
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| author | Chen, T Forejt, V Kwiatkowska, M Simaitis, A Wiltsche, C |
| author_facet | Chen, T Forejt, V Kwiatkowska, M Simaitis, A Wiltsche, C |
| author_sort | Chen, T |
| collection | OXFORD |
| description | We study two-player stochastic games, where the goal of one player is to satisfy a formula given as a boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and veri cation of open systems with stochastic behaviour. We show that nding a winning strategy is PSPACE-hard in general and undecidable for deterministic strategies. We also prove that optimal strategy, if such exists, may require in nite memory and randomisation. However, when restricted to disjunctions of objectives only, memoryless deterministic strategies suffice, and the problem of deciding whether a winning strategy exists is NP-complete. We also present algorithms to approximate the Pareto sets of achievable objectives for the class of stopping games. |
| first_indexed | 2024-03-07T04:16:01Z |
| format | Report |
| id | oxford-uuid:c97287e3-0f85-40e7-879f-6bb3378da8f4 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:16:01Z |
| publishDate | 2013 |
| publisher | DCS |
| record_format | dspace |
| spelling | oxford-uuid:c97287e3-0f85-40e7-879f-6bb3378da8f42022-03-27T06:59:10ZOn Stochastic Games with Multiple ObjectivesReporthttp://purl.org/coar/resource_type/c_93fcuuid:c97287e3-0f85-40e7-879f-6bb3378da8f4Department of Computer ScienceDCS2013Chen, TForejt, VKwiatkowska, MSimaitis, AWiltsche, CWe study two-player stochastic games, where the goal of one player is to satisfy a formula given as a boolean combination of expected total reward objectives and the behaviour of the second player is adversarial. Such games are important for modelling, synthesis and veri cation of open systems with stochastic behaviour. We show that nding a winning strategy is PSPACE-hard in general and undecidable for deterministic strategies. We also prove that optimal strategy, if such exists, may require in nite memory and randomisation. However, when restricted to disjunctions of objectives only, memoryless deterministic strategies suffice, and the problem of deciding whether a winning strategy exists is NP-complete. We also present algorithms to approximate the Pareto sets of achievable objectives for the class of stopping games. |
| spellingShingle | Chen, T Forejt, V Kwiatkowska, M Simaitis, A Wiltsche, C On Stochastic Games with Multiple Objectives |
| title | On Stochastic Games with Multiple Objectives |
| title_full | On Stochastic Games with Multiple Objectives |
| title_fullStr | On Stochastic Games with Multiple Objectives |
| title_full_unstemmed | On Stochastic Games with Multiple Objectives |
| title_short | On Stochastic Games with Multiple Objectives |
| title_sort | on stochastic games with multiple objectives |
| work_keys_str_mv | AT chent onstochasticgameswithmultipleobjectives AT forejtv onstochasticgameswithmultipleobjectives AT kwiatkowskam onstochasticgameswithmultipleobjectives AT simaitisa onstochasticgameswithmultipleobjectives AT wiltschec onstochasticgameswithmultipleobjectives |