We study continuous-time stochastic games with time-bounded reachability objectives. We show that each vertex in such a game has a \emph{value} (i.e., an equilibrium probability), and we classify the conditions under which optimal strategies exist. Finally, we show how to compute optimal strategies in finite uniform games, and how to compute $\varepsilon$-optimal strategies in finitely-branching games with bounded rates (for finite games, we provide detailed complexity estimations).
@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2307, author = {Brazdil, Tomas and Forejt, Vojtech and Krcal, Jan and Kretinsky, Jan and Kucera, Antonin}, title = {{Continuous-Time Stochastic Games with Time-Bounded Reachability}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {61--72}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2307}, URN = {urn:nbn:de:0030-drops-23077}, doi = {10.4230/LIPIcs.FSTTCS.2009.2307}, annote = {Keywords: Continuous time stochastic systems, time bounded reachability, stochastic games} }
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