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Qualitative Concurrent Stochastic Games with Imperfect Information

V. Gripon and O. Serre, "Qualitative Concurrent Stochastic Games with Imperfect Information," in Proceedings of 36th International Colloquium of Automata, Languages and Programming, Springer, Lecture Notes in Computer Science, Rhodes, Greece, pp. 200--211, July 2009.

We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability distribution depending on the previous state and on the pair of actions chosen by the players. Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs. Therefore, if two partial plays are indistinguishable by some player, he should behave the same in both of them. We consider reachability (does the play eventually visit a final state?) and Buchi objective (does the play visit infinitely often a final state?). Our main contribution is to prove that the following problem is complete for 2-ExpTime: decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her oponent. We also characterise those strategies needed by the first player to almost-surely win.

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Bibtex
@inproceedings{GriSer20097,
  author = {Vincent Gripon and Olivier Serre},
  title = {Qualitative Concurrent Stochastic Games
with Imperfect Information},
  booktitle = {Proceedings of 36th International
Colloquium of Automata, Languages and Programming},
  year = {2009},
  editor = {Springer},
  pages = {200--211},
  series = {Lecture Notes in Computer Science},
  address = {Rhodes, Greece},
  month = {July},
}




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