Continuous Capacities on Continuous State Spaces

  • Jean Goubault-Larrecq
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

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.

Keywords

Markov Decision Process Stochastic Game Belief Function Convex Game Continuous State Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jean Goubault-Larrecq
    • 1
  1. 1.LSV, ENS Cachan, CNRS, INRIA Futurs, 61, avenue du président-Wilson, F-94235 Cachan 

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