2007 | OriginalPaper | Chapter
Continuous Capacities on Continuous State Spaces
Author : Jean Goubault-Larrecq
Published in: Automata, Languages and Programming
Publisher: Springer Berlin Heidelberg
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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.