We propose axiomatizing some stochastic games, in a continuous state space setting, using continuous belief functions, resp. plausibilities, instead of measures. Then, stochastic games are just variations on continuous Markov chains. We argue that drawing at random along a belief function is the same as letting the probabilistic player P play first, then letting the non-deterministic player C play demonically. The same holds for an angelic C, using plausibilities instead. We then define a simple modal logic, and characterize simulation in terms of formulae of this logic. Finally, we show that (discounted) payoffs are defined and unique, where in the demonic case, P maximizes payoff, while C minimizes it. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Goubault-Larrecq, J. (2007). Continuous capacities on continuous state spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4596 LNCS, pp. 764–776). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_66
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